#### Answer

17m

#### Work Step by Step

The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$.
This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$
The walkway forms the hypotenuse of a right triangle, which is given as 24m. The playground is square, so each side of the right triangle can be represented by x.
Substitute x in for a and b and 24 in for c.
$a^{2}$+$b^{2}$=$c^{2}$
$x^{2}$+$x^{2}$=$24^{2}$
2$x^{2}$=576
Divide both sides by 2.
$b^{2}$=288
Take the square root of both sides to find the length of the sides of the playground.
b=16.970
Round to the nearest meter
17m