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^{circ}-45^{circ}-90^{circ} ) triangle theorem, find the value of ( h ), the height of the wall. ( 6.5 mathrm{ft} ) ( 6.5 sqrt{2} mathrm{ft} ) ( 13 mathrm{ft} ) ( 13 sqrt{2} mathrm{ft} )

Explanation:

Step1: Recall the 45° - 45° - 90° triangle ratio

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

Step2: Set up the equation using the hypotenuse length

We are given that the hypotenuse of the right - triangle (part of the trapezoid) is \(13\sqrt{2}\) ft. If \(x\sqrt{2}=13\sqrt{2}\) (where \(x = h\) since the leg of the right - triangle is equal to the height \(h\) of the trapezoid).
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