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. diagram: trapezoid with rectangle and right triangle, dashed line ( h ), hypotenuse ( 13sqrt{2} ) ft, angle ( 45^circ ) using the ( 45^circ\text{-}45^circ\text{-}90^circ ) triangle theorem, find the value of ( h ), the height of the wall.
○ ( 6.5 ) ft
○ ( 6.5sqrt{2} ) ft
○ ( 13 ) ft
○ ( 13sqrt{2} ) ft

Explanation:

Step1: Recall 45-45-90 triangle ratios

In a \(45^\circ\)-\(45^\circ\)-\(90^\circ\) triangle, the legs are equal, and the hypotenuse \(c = l\sqrt{2}\), where \(l\) is the length of a leg.

Step2: Relate hypotenuse to leg (height \(h\))

Given hypotenuse \(= 13\sqrt{2}\) ft. Let \(h\) be the leg (height). Using \(c = l\sqrt{2}\), we solve for \(l\) (which is \(h\)):
\(13\sqrt{2}=h\sqrt{2}\)
Divide both sides by \(\sqrt{2}\): \(h = 13\) ft.

Answer:

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