Suppose that the combined area of two squares is 360 square feet. Each side of the larger square is three times as long as a side of the smaller square. How big is each square?

ruigE 2021-02-09 Answered
Suppose that the combined area of two squares is 360 square feet. Each side of the larger square is three times as long as a side of the smaller square. How big is each square?
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Expert Answer

odgovoreh
Answered 2021-02-10 Author has 107 answers

Let x be the side length of the larger square and yy be the side length of the smaller square.
The area of a square is s2 where ss is the side length so the larger square has an area of x2 and the smaller square has an area of y2. The combined area is then x2+y2. If the combined area is 360 square feet then x2+y2=360.
If the side of the larger square is three times as long as the side of the smaller square, then x=3y.
Substitute x=3y into x2+y2=360 and solve for y:
x2+y2=360
(3y)2+y2=360
9y2+y2=360
10y2=360
y2=36
y2=±36
y=±6
Since the sides of the squares must be positive, then y=6 so x=3y=3(6)=18. The larger square then has side lengths of 18 ft and the smaller square has side lengths of 6 ft.

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Jeffrey Jordon
Answered 2021-08-10 Author has 2495 answers

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