18. Architecture A special window has the shape of arectangle surmounted by an equilateral triangle. See thefigure. If the perimeter of the window is 16 feet, whatdimensions will admit the most light?[Hint: Area of an equilateral triangle =is the length of a side of the triangle.](웃), where x

Let x be the length of rectangle and y be the breadth of the rectangle . The side of triangle is…

Answered: 18. Architecture A special window has…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter3: Solving Equation And Problems

Section3.8: Proof In Algebra

Problem 1ST

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Similar questions

Geometry What are the dimensions of a right triangle with a two-inch hypotenuse and an area of 1 square inch?
The Turners want to install outdoor carpet around their rectangular pool. The dimensions for the rectangular area formed by the pool and its walkway are 20 ft by 30 ft. The pool is 12 ft by 24 ft. aHow many square feet need to be covered? bApproximately how many square yards does the area in part a represent? cIf the carpet costs 12.95 per square yard, what will be the cost of the carpet?
Enclosing a field You have 16 miles of fence that you will use to enclose a rectangle field. a.Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 3 miles and length 5 miles. What is the area of this rectangle? b.Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 2 miles and length 6 miles. What is the area of this rectangle? c.The first two parts of this exercise are designed to show you that you can get different areas for the rectangle of the sane perimeter, 16 miles. In general, if you arrange the 16 miles of fence into a rectangle of width w miles, then it will enclose an area of A=w8-w square miles. iMake a graph of the area enclosed as a function of w, and explain what the graph is showing. iiWhat width w should you use to enclose the most area? iiiWhat is the length of the maximum-area rectangle that you made, and what kind of figure do you have?
Dimensions of a Garden A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens (see figure). The gardener wants the enclosed area to be 350 square meters. What dimensions should the gardener use to obtain this area ?
Look at the two figures below. (a) Which figure looks like it has the larger area? Which looks like it has the larger perimeter? (b) Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter? (c) Were the results of part (b) the same as your answers in part (a)? Is that surprising to you?
Edging a Planter A woman wants to make a small planter and surround it with edging material. She is deciding between two designs. Design 1: A square planter Design 2: A circular planter Edging material costs 3 a foot for the straight variety, which she would use for design 1 and 4 a foot for the flexible variety, which she would use for design 2. a If she decides on a perimeter of 24 ft, which design would give her the larger planting area? b If she decides to spend 120 on edging material, which design would give her the larger planting area?
Width of a Lawn A factory is to be built on a lot measuring 180 ft by 240 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be, and what are the dimensions of the factory?

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