)A wire of length L is cut into pieces, one being bent to form a square and the other o form an equilateral triangle. How the wire should be cut: -) if the sum of the two areas is minimum. ) if the sum of the two areas is maximum

)A wire of length L is cut into pieces, one being bent to form a square and the other o form an equilateral triangle. How the wire should be cut: -) if the sum of the two areas is minimum. ) if the sum of the two areas is maximum

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.2: The Parallelogram And Kite

Problem 5E: A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If...

See similar textbooks

Related questions

Q: 4. The sides of a triangular lot are 130 m, 180 m, and 190 m. The lot is to be divided by a line…

A: Cosine law

Q: 9. DABCD is a convex quadrilateral. Let P, Q, R, S be centers of the squares drawn (externally to…

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.

A: 1) Opposite sides are equal , 2) The diagonals of a rectangle are equal. Distance formula of point…

Q: Must be in a paragraph proof

A: Given: ABC is a right triangle and BEDF is a square. Since, BEDF is a square with DF=x, so all of…

Q: Consider a radix 3 (possibly non-linear) code C of length n = 5 and minimum distance d(C) = 5. What…

A: In sphere packing bound, the code length is is 1 greater than the value of C. i.e. Covering radius…

Q: Given: BC || AD and AB || CD. Prove: /BCD /BAD. Note: quadrilateralproperties are not pemitted in…

Q: Three spheres, with radius R and lie in the same plane, are given such that each of the spheres…

A: Given, The radius of three sphere is From the given information we can draw the below diagram,

Q: The Converse of the Corresponding Angles Theorem states that if two coplanar lines are cut by a…

A: The theorem of converse of correspondingangles : If two parallel lines are cut by a transversal,…

Q: 3. Conduct a formal proof to prove that the diagonals of an isosceles trapezoid are congruent.

A: Given: Consider the isosceles trapezoid ABCD shown below: AB=CD To prove: AC≅BD

Q: 2. If there are seven distinct points on a plane with no three are collinear, how many different…

A: A polygon requires at least 3 points (and 3 sides). Since no 3 points are collinear, that means you…

Q: 2. Prove that if the Fermat-Torricelli point of an acute triangle ABC coincides with the incenter,…

Q: 45. Prove: If the diagonals of a trapezoid are congru- ent, then it is an isosceles trapezoid.

A: Prove:- if the diagonals of a trapezoid are congruent, then it is an isosceless trapeziod Now given…

Q: 9. Prove, by coordinate geometry that QRST is a parallelogram. Q(0

Q: If there are 7 distinct points on a plane with no three of which are collinear, how many different…

A: The number of ways r items can be selected from n distinct items is equal to Cn, r. The formula for…

Q: 10. Prove that quadrilateral A(1,-2), B(13,4), C(6,8) and D(-2,4) is a trapezoid, but is NOT an…

Q: the polygon is convex, then the sum of its interior angles is

A: if a convex polygon has n sides ,then its interior angle sum is given by the following equation

Q: 3. Consider an acute angled triangle ABC and a point D on BC. Find points (by construction) E on AC…

A: Given: An acute angled triangle ,inscribe in it a triangle whose perimeter is minimum.…

Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle

Q: アon) usweris X10 बप्कणs In the ry-plane, what is the perimeter of an equilateral triangle with one…

Q: . Prove that in a triangle, the orthocenter, centroid and the circumcenter are concurrent (in a…

A: Let X be the mid-point of EF Construct the median DX. Since G is the centroid, G is on DX by the…

Q: 1. Which pair of triangles cannot be proven congruent using the HL theorem? ок M

A: The given pairs of triangles are given as

Q: What type of polygon must have a diagonal such that at least part of the diagonal falls in the…

A: It is known that, a quadrilateral is a plane figure that is made up of four line segments closing in…

Q: The vertices of quadrilateral KAIT are K(0,0), A(a, 0), I(a + b, c), and T(b, c). Use coordinate…

A: Parallelogram is a kind of quadrilateral with two pairs of opposite sides. In a parallelogram, the…

Q: paragraph proof please!

A: Given: Points P, Q, R and S are the mid-points of sides of isosceles trapezium ABCD with AB || CD…

Q: IFA and B have 6 and 9 elements each, what is the minimum number of elements Aunion B?*

Q: 1. The circular track is tangent to each side of Quadrilateral ABCD, and all of the angles in…

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: In ACDE, CE is extended through point E to point F, mZCDE = (2x – 4)°, mZDEF = (6x – 10)°, and mZECD…

A: Given: ∠CDE=(2x-4)°∠DEF=(6x-10)°∠ECD=(2x+16)°

Q: 1. Given: Quadrilateral POST is an isosceles trapezoid with OS || PT. ER is its median. a. If OS =…

A: Draw the diagram and use the property of isosceles trapezoid.

Q: ABCD is a quadrilateral and G, H are the middle points of AC, DB. If CB, DA are produced to meet in…

Q: Prove that the base of a Saccheri Quadrilateral in absolute geometry has length less than or equal…

Q: 1. Sketch an example of a convex heptagon and an example of a concave heptagon.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. If two triangles are to be proven congruent using a postulate, what is the least number of parts…

A: Two triangles are said to be congruent if corresponding sides and corresponding angles are equal in…

Q: 2. Show that if two sides of a cyclic quadrilateral are parallel, then the other two sides are of…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: nany triangles can be drawn ar points?

A: In this question, the concept of Combination is applied. Combination A combination is a mathematical…

Q: E. Prove that if semicircles are constructed on each of the sides of a right triangle, then the area…

A: In triangle ABC, using pythagorus theorem - c2 = a2+b2 .............(1)Semicircle on…

Q: Prove that of all triangles having two given sides of lengths a and b, the one whose sides form a…

A: It is given that the length of two sides of a triangle is a and b, respectively. It is known that…

Q: Give all possible integer values of x so that a pentagon with interior angle measures in the ratio…

Q: The Converse of the Corresponding Angles Theorem states that if two coplanar lines are cut by a…

Q: 1. Prove analytically that the lines joining the midpoints of the adjacent sides of the…

Q: 4 the epatin rus ts of quadrahe 22+ Cm +)x +n Gve Iaomd 3 find the Ualues of

Q: Based on triangulation of polygons, prove that copies of a regular n- gon can tile the plane only…

Q: %23 W Two sets of rails (railroad tracks are equally spaced) intersect but not at right angles.…

Q: It is about proofs.

A: Draw a circle. Let AB is the diameter. AC and BD are two chords from the ends of the diameter so…

Q: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of…

A: Area of semi circle having diameter of a is, Aa=πa222Aa=πa28 ...(1) Area of semi circle…

Q: Given kite ABCD and isosceles trapezoid WXYZ, complete a two-column proof to show that △ADW ≅ △CDZ

A: Kite- ABCD isoceles trapezoid- WXYZ show △ADW≅△CDZ

Q: How many planes of symmetry does a polyhedron with 2 square bases and eight isosceles triangle…

Q: 25. Given: Quadrilateral PQST with midpoints A, B, C, and D of the sides Prove: ABCD is a O

Q: Suppose that A, B, C, D and A′, B′, C′, D′ (in those orders) form the vertices of convex…

A: Consider the given: Given:AB=A'B'In a parallelogram, parallel sides have equal length.In…

Q: Prove that if two pairs of opposite edges of a tetrahedron are perpendicular, then the third pair is…

A: Consider the tetrahedron ABCD and let two pairs of opposite sides are perpendicular. Consider the…

Question

)A wire of length Lis cut into pieces, one being bent to form a square and the other
o form an equilateral triangle. How the wire should be cut:
) if the sum of the two areas is minimum.
p) if the sum of the two areas is maximum

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Basics (types, similarity, etc)$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of the semicircle on the hypotenuse is equal to the sum of the areas of the semicircles on the two legs.
Which of these two polyhedrons is concave? Note that the interior dihedral angle formed by the planes containing EJF and KJF is larger than 180 .
a Is it really necessary to construct all three bisectors of the angles of a triangle to locate its incenter? b Is it really necessary to construct all three perpendicular bisectors of the sides of a triangle to locate its circumcenter?
Two sets of rails railroad tracks are equally spaced intersect but not at right angles. Being as specific as possible, indicate what type of quadrilateral WXYZ is formed.
A trapezoid is a four-sided figure that contains one pair of parallel sides. Which sides of the trapezoid MNPQ appear to be parallel?
In Exercises 39 and 42, refer to the line segments shown. Use the following theorem to construct a triangle similar to the given triangle but with sides that are twice the length of those of the given triangle. Theorem: If the lengths of the three pairs of sides for two triangles are in proportion, then those triangles are similar SSS.
Given: B is the midpoint of AC BDAC Prove: ADC is isosceles
A quadrilateral RSTV is circumscribed about a circle so that its tangent sides are at the endpoints of two intersecting diameters. aWhat types of quadrilateral is RSTV? bIf the diameters are also perpendicular, what type of quadrilateral is RSTV?
In the three-dimensional figure, CAAB and BEAB. Are CAandBE parallel to each other? Compare with Exercise 6.
Let all of the lines named be coplanar. Make a drawing to reach a conclusion. a If rs and st, then _. b If ab and bc, then _.
In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._
A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If these are joined at the ends to form a quadrilateral that has the 8-ft pieces connected in over, what type of quadrilateral is formed? b If these are joined at the ends to form a quadrilateral that has the 4-ft and 8-ft pieces alternating, what type of quadrilateral is formed?