Chapter 6.7, Problem 62HP

To determine

To Find The length of the support.

Answer to Problem 62HP

Thelength of the support is $4\sqrt{3}$ .

Explanation of Solution

Given:

Theshape of the window is equilateral triangle.

The side of the triangle is 8 feet long.

The window is divided in half by the support from one vertex to the midpoint of the side of the triangle of the opposite vertex.

Calculation:

Consider the figure for the window is shown in Figure 1

  

Figure 1

From above figure,

  $\begin{array}{c}\angle AMB=\angle AMC\\ =\frac{180°}{2}\\ =90°\end{array}$

The triangle AMB is congruent to AMC and AM is common side then,

  $\begin{array}{l}MB=MC\\ AB=AC\end{array}$

The side is of 8 feet then,

  $\begin{array}{c}BM=MC\\ =\frac{BC}{2}\\ =\frac{8}{4}\\ =2\end{array}$

Then, the length of AM is obtained as,

  $\begin{array}{c}AM=\sqrt{A{B}^2-B{M}^2}\\ =\sqrt{8^2-4^2}\\ =4\sqrt{3}\end{array}$