Chapter 11, Problem 37CUR

To determine

To Find:

1. The perimeter of $\Delta ACD$ .
2. The ratio of areas of $\Delta ABE$ and $\Delta ACD$ .

Answer to Problem 37CUR

1. 46
2. $\frac{1}{4}$

Explanation of Solution

Given:

  $B$ and $E$ are the mid points of $\overline{AC},\overline{AD}$ .

  $AB=9,BE=6,AE=8$

  

Given that: $B$ and $E$ are the mid points of $\overline{AC},\overline{AD}$ .

Therefore,

  $\begin{array}{l}AB=BC=9,AE=ED=8\\ \Rightarrow AC=18,AD=16\end{array}$

According to Mid-point theorem:

  $BE\left|\right|CD$

  $\begin{array}{l}BE=\frac{1}{2}CD\\ \Rightarrow CD=12\end{array}$

Perimeter of a triangle is given as sum of all the sides.

So, perimeter of $\Delta ACD$ =18+16+12=46

Ratio of two similar triangles is equal to the ratio of square of any corresponding sides.

The ratio of areas of $\Delta ABE$ and $\Delta ACD$ = $\frac{9^2}{{18}^2}=\frac{1}{4}$