Long shot distance

Question

to avoid hitting the ball out, a tennis player in one corner of the 312 yd^2 court hits the ball to the furthest corner of the opponent's court as shown in the diagram. If the length L of the tennis court is 2 yd longer than twice the width W, then how far did the player hit the ball?

Answer 1

Let Length = L = 2 + 2W

Area = 312
Area = length x width

312 = (2+2W)W = 2W + 2W²

divide by 2 and rearrange

W² + W - 156 = 0

quadratic has two solutions

(W-12)*(W+13) = 0

W = 12 is one solution and L = 2+2W = 26 yards

Use Pythagorean Theorem to find the diagonal as sqrt(12² + 26²) = 28.64 yds