a wall in marias bedroom is in the shape of a trapezoid. the wall can be divided into a rectangle and a…

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

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

Answer

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the hypotenuse $c$ is related to the legs $a$ and $b$ (which are equal) by $c = a\sqrt{2}$.

Step2: Set up equation for hypotenuse

Let the height of the triangle (which is the same as the height $h$ of the wall) be $x$. The hypotenuse of the 45 - 45 - 90 triangle is given as $13\sqrt{2}$ ft. Using the ratio $c=a\sqrt{2}$, we have $13\sqrt{2}=x\sqrt{2}$.

Step3: Solve for $x$ (height $h$)

Divide both sides of the equation $13\sqrt{2}=x\sqrt{2}$ by $\sqrt{2}$. So, $x = 13$ ft.

Answer:

C. 13 ft