A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a side. If the process is continued until there are already six squares, find the sum of the areas of all squares in square inches.

Q: Find the dimensions of the largest rectangle that can be inscribed in an isosceles triangle if one…

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Q: A 40­inch board is to be cut into three pieces so that thesecond piece is twice as long as the first…

A: Let the length of first piece is x inches. The length of second piece is twice as long as the first…

Q: Show that among all rectangles with an 8-m perimeter, the one with largest area is a square.

A: Let l be the length and b be the breadth of the rectangle.

Q: Find the area of the largest rectangle that can be inscribed in a right triangle with legs of…

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Q: Exactly three faces of a 2x2x2 cube are partially shaded, as shown. (Each of the three faces not…

A: All sides of a cube are of equal length. If the side length of a cube is a , then the surface area…

Q: Find two positive integers such that the sum of the first and five times the second number is 2000…

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Q: Find three positive numbers whose sum is 36 and such that the sum of their squares is as small as…

A: Solution is given below:

Q: Suppose that we are given a rectangular box with a length of 8 centimeters, a width of 6…

A: Given: The length of a rectangular box is 8 cm, width is 6 cm and height is 4 cm. To find: The…

Q: A yellow square of side 1 is divided into nine smaller squares, and the middle square is colored…

A: The length of the side of the outer most yellow square is 1 unit and the area is 1 sq unit. And…

Q: A rectangle piece of a metal has a length that is 10 inch longer than it’s width. Squares with sides…

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Q: How many workers will be needed to complete a task in 8 days, given that 4 workers can complete the…

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Q: Find the area of the largest rectangle that can be inscribed in a right triangle withe legs of…

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Q: Fill a 4X4 magic square with real numbers so that the product of the numbers in each row is less…

A: For finding the required answer first construct the magic square with order 4.…

Q: The hypotenuese of an isosceles right triangle is 9 inches. The midpoints of its sides are connected…

A: Given: In isosceles right-angled triangle, hypotenuse is 9 inches and the midpoint of each sides…

Q: if a triangle is inscribed in a circle so that one of the triangle side is a diameter of a circle,…

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Q: A certain city block is in the form of a parallelogram. Two of its sides are each 140 m long; the…

A: The given city is in the form of the parallelogram given below.

Q: An athletes runs with velocity 11 km/h for 4 minutes, 14 km/h for the next 2 minutes, and 17 km/h…

A: Use the velocity distance formula given below, d=v×t where d is the distance, v is the velocity (in…

Q: A rectangle is inscribed in a right triangle. If the triangle has sides of length 5, 12, and 13,…

A: Let x and y be the length and breadth of the rectangle inscribed in the triangle. Let us take the…

Q: Find the dimensions of the largest rectangle that can be inscribed in the right triangle with side…

A: Area of rectangle= length×bredth

Q: A shipping company handles rectangular boxes provided the sum of the length, width, and height of…

A: Let the dims be x, y and z then volume V=xyz           -----------(1) and the restriction we have…

Q: If in a rectangle the length is increased and breadth is decreased by 2 units each, the area is…

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Q: Find three consecutive odd integers such that the product of the first and the second is 8 more than…

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Q: A rectangle piece of Metal has a length that is 10 inch longer than its width. Squares with sides 3…

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Q: Suppose a rectangular picture frame has a thin border made from a 144-inch-long strip of bronze. If…

A: # Considering the width of border negligible Length of the strip is 144 inch Now let the length of…

Q: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.…

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Q: Find three consecutive odd intergers such that the product of the two larger numbers is 18more than…

A: To form the equation satisfied by the required integers  and therby solve for them

Q: The sides of a right triangle are 8, 15 and 17 units. If each side is 1.5 times larger than original…

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Q: A farmer with 450 ft of fencing wants to enclose a rectangular area and then divide it into 3 pens…

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Q: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four…

A: Solution: Let x be the width of the rectangle and y the height. we can form the equation  5x +…

Q: A box with an open top is to be constructed from a square piece of cardboard 2m inches wide, by…

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Q: Show that the sum of a positive number and its reciprocal is at least 2.

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Q: Find the area(square meters) of the largest rectangle that can be inscribed in an equilateral…

A: The rectangle is inscribed in an equilateral triangle of side 2 meters. The one side of the…

Q: When a rubber ball falls, it rebounds to a height 60% of the height from which it dropped. If the…

A: SOLUTION-

Q: The bacteria in a petri dish grow in a manner such that each day the number of bacteria doubles. On…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: . Find two positive integers such that the sum of the first number and four times the second number…

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Q: Suppose there are two rectangular pools: one is 30 feet wide, 60 feet long and 5 feet deep…

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Q: Suppose that the 149 million square kilometers of land on the surface of the earth was divided…

A: Given: Area of the land on the surface of the earth A=149 million square kilometers. Area divided…

Q: An open-topped box can be created by cutting congruent squares from each of the four corners of a…

A: Given, l= 30-2x b= 20-2x h= x Volume= 1008 cm³

Q: if an open box is made from a tin sheet 7 in. square by cutting out identical squares from each…

A: Given that a open box made from a tin sheet 7 inch.and determine largest box that can be made. Here…

Q: find three consecutive odd integers such that the sum of the first and the second is sixteen more…

A: Given:The three consecutive integers are odd numbers.The sum of the first two consecutive odd number…

Q: A rectangular box is to be made from a square piece of cardboard of side length 10 inches by cutting…

A: We need to determine dimension of box.

Q: An open box is to be made from a square piece of cardboard,18 inches by 18 inches, by cutting out…

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Q: A farmer with 750 ft of fencing wants to enclose a rectangular region and then divide it into four…

A: Solve for the lager rectangle dimension and area of large rectangle

Q: A 6 cm by 15 cm by 18 cm rectangular prism is cut into three pieces that are 1/2, 1/3, and 1/6 of…

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Q: Find the three consecutive integers such that that product of the first and third is one less than…

A: Take three consecutive integer as below :n-1, n , n+1

Q: a farmer with 750 feet of fencing wants to enclose a rectangular area and then divide it into four…

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Q: A 10ft board is to be cut into three pieces, two equal-length ones and the third 3 in. Shorter than…

A: Calculation:It is given that the length of a board is 10ft which has to be cut into three…

Q: Find two positive integers such that the sum of the first number and four times the second number is…

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Q: Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given…

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Q: Suppose it takes 10 hours to fill a rectangular swimming pool of uniform depth. How long will it…

A: Solve using flow rate.