Use the Pythagorean Theorem to find the unknown lengths

x =

Based on the pythagorean theorem we know:

x^{2} + (x + 2)^{2} =

x^{2} + x^{2} + 4x + 4 = 10

2x^{2} + 4x – 6 = 0

2(x – 1)(x + 3) = 0

x = 1^{ }and^{ }x = -3

Since lengths must be positive, x = 1