Chapter 9.8, Problem 3PSA

To determine

To find: The Value of altitude and slant height.

Answer to Problem 3PSA

The Measure of altitude and slant height is $5\sqrt{3}$ and $10$ respectively.

Explanation of Solution

Given information:$\overline{AF}$ is slant height, $\overline{AG}$ is altitude, Perimeter of BCDE is $40$ and $\angle AFG$ is $60°$

Calculation: As, Perimeter of BCDE is $40$ ,

  $\Rightarrow \overline{BC}=\frac{40}{4}=10$

Now, $\overline{BC}=10$ ,

  $\Rightarrow \overline{FG}=\frac{10}{2}=5$ (As, altitude bisects the base)

Now, in $\Delta AFG$ ,

Angles are $90°,60°,30°$ ,

  $\Rightarrow$ Hypotenuse = $2a$

and other two sides will be $a$ and $a\sqrt{3}$ respectively.

Now, as one side is $5$ ,

  $\Rightarrow$ Other side (Altitude) = $5\sqrt{3}$

Hypotenuse (Slant height) = $2\times 5=10$ .