17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.
The key to solve this problem is using the Pythagorean Theorem that dictates; In every right triangle the square of the hypotenuse is equal to the sum of the squares of the legs and the equation hypotenuse²=leg1²+leg2².
For this problem we know the measuring of two side, which mean that we can apply Pythagorean Theorem equation as follow:
Let's say that one of the side is a = 8yards, and the other side is b = 15yards. So, we want to know how long the third side c long.
Applying the Pythagorean Theorem:
![c^{2} =a^{2}+b^{2} \\c=\sqrt{a^{2}+b^{2}}](https://tex.z-dn.net/?f=c%5E%7B2%7D%20%3Da%5E%7B2%7D%2Bb%5E%7B2%7D%20%20%5C%5Cc%3D%5Csqrt%7Ba%5E%7B2%7D%2Bb%5E%7B2%7D%7D)
Substituting the values of the sides a and b:
![c=\sqrt{(8yards)^{2}+(15yards)^{2}}\\c=\sqrt{64yards^{2}+225yards^{2}}\\c=\sqrt{289yards^{2}}\\c=17yards](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B%288yards%29%5E%7B2%7D%2B%2815yards%29%5E%7B2%7D%7D%5C%5Cc%3D%5Csqrt%7B64yards%5E%7B2%7D%2B225yards%5E%7B2%7D%7D%5C%5Cc%3D%5Csqrt%7B289yards%5E%7B2%7D%7D%5C%5Cc%3D17yards)