# Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 23

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

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