Question

The total area of two square windows is 1,025 in.2. Each side of the larger window is 5 in. longer than the sides of the smaller window. How long are the sides of the smaller window?

A = s2
13.5 in.
20 in.
25 in.
31.6 in.

Answer 1

Let the smaller side be s. Then s^2 + (s+5)^2 = 1025.

2s^2 + 10s + 25 = 1025 → 2s^2 + 10s - 1000 = 0 → s^2 + 5s - 500 = 0.

s = [-5 ± √(25 + 2000)]/2 = [-5 ± 45]/2, so s = 20 (negative root discarded).

Answer: 20 in.