Question

Solve for the legs of the 45-45-90 triangle.

Answer 1

1st answer option

Explanation:

the 45° side angles make this an isoceles triangle (both legs are equally long).

therefore, x = y.

Pythagoras gives us

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a and b being the legs.

so, we have

(5 × sqrt(2))² = x² + y² (remember, x = y)

(5 × sqrt(2))² = x² + x²

25 × 2 = 2x²

25 = x²

x = 5

because of x = y

y = 5