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. using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall. 6.5 ft, 6.5√2 ft, 13 ft, 13√2 ft

Explanation:

Step1: Recall 45°-45°-90° triangle theorem

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the legs are equal, and the hypotenuse \(c\) is related to the leg \(a\) (or \(b\)) by the formula \(c = a\sqrt{2}\), so \(a=\frac{c}{\sqrt{2}}\).

Step2: Identify the triangle components

The triangle in the diagram is a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle with hypotenuse \(c = 13\sqrt{2}\) ft, and \(h\) is one of the legs.

Step3: Calculate \(h\)

Using the formula \(a=\frac{c}{\sqrt{2}}\), substitute \(c = 13\sqrt{2}\):
\[
h=\frac{13\sqrt{2}}{\sqrt{2}} = 13
\]

Answer:

13 ft (corresponding to the option "13 ft")