Question

a wall in marias 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 the 45 - 45 - 90 triangle theorem

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\). Let the legs of the right - triangle (the sides opposite the 45° angles) be \(x\) and \(x\), and the hypotenuse be \(x\sqrt{2}\).

Step2: Set up the equation using the hypotenuse value

We are given that the hypotenuse of the 45 - 45 - 90 triangle is \(13\sqrt{2}\) ft. According to the 45 - 45 - 90 triangle formula \(c=x\sqrt{2}\) (where \(c\) is the hypotenuse and \(x\) is the length of each leg).
If \(c = 13\sqrt{2}\), then \(x\sqrt{2}=13\sqrt{2}\). Solving for \(x\) (where \(x = h\) in our problem, since \(h\) is the leg of the 45 - 45 - 90 triangle), we divide both sides of the equation \(x\sqrt{2}=13\sqrt{2}\) by \(\sqrt{2}\).

$$x=\frac{13\sqrt{2}}{\sqrt{2}}=13$$

Answer:

\(13\) ft