Chapter 15, Problem 9CR

To determine

To Find: The length of the required segment in the given figure.

Answer to Problem 9CR

  $42$

Explanation of Solution

Given:

  $\begin{array}{l}B\&E\text{ are mid-points of }\overline{AC}\&\overline{AD}\text{ respectively}\\ BE=2.5x\\ CD=5.2x\end{array}$

  

Formula Used:

Mid-Segment Theorem: It states that segment joint to two sides of triangle is parallel to the third side of the triangle and half as long.

Calculation:

  $\begin{array}{l}B\&E\text{ are mid-points of }\overline{AC}\&\overline{AD}\text{ respectively}\\ BE=2.5x\\ CD=5.2x\\ BE=\frac{1}{2}CD\\ 5-2x=\frac{1}{2}\left(2-5x\right)\\ \text{⇒}5-2x=1-\frac{5}{2}x\\ \text{⇒}\frac{5}{2}x-2x=1-5\\ \text{⇒}\frac{1}{2}x=-4\\ \text{⇒}x=-8\\ CD=2-5\left(-8\right)=2+40=42\end{array}$

Conclusion:

Thus the required length of segment is $42$ .