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.

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.