Question

A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle.

A trapezoid is shown. A straight line with length h is drawn to the opposite side to form a right angle. It splits the shape into a rectangle and a triangle. The length of the hypotenuse is 13 StartRoot 2 EndRoot feet. The other angles of the triangle are 45 degrees.

Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.

6.5 ft
6.5 StartRoot 2 EndRoot ft
13 ft
13 StartRoot 2 EndRoot ft

Answer 1

In a 45°-45°-90° triangle the hypotenuse = leg × √2. So each leg = hypotenuse ÷ √2 = (13√2) ÷ √2 = 13.

Thus h = 13 ft.