Question

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?

Quadratic function and equation
ANSWERED
asked 2021-02-09
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?

Answers (2)

2021-02-10
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 \(\displaystyle{s}^{{{2}}}\) where ss is the side length so the larger square has an area of \(\displaystyle{x}^{{{2}}}\) and the smaller square has an area of \(\displaystyle{y}^{{{2}}}\). The combined area is then \(\displaystyle{x}{2}+{y}^{{{2}}}\). If the combined area is 360 square feet then \(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={360}.\)
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 \(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={360}\) and solve for y:
\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={360}\)
\(\displaystyle{\left({3}{y}\right)}^{{{2}}}+{y}^{{{2}}}={360}\)
\(\displaystyle{9}{y}^{{{2}}}+{y}^{{{2}}}={360}\)
\(\displaystyle{10}{y}^{{{2}}}={360}\)
\(\displaystyle{y}^{{{2}}}={36}\)
\(\displaystyle\sqrt{{y}}^{{{2}}}=\pm\sqrt{{36}}\)
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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2021-08-10

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