Chapter SR22, Problem 16P

Solution

The two polygons are similar. Find the value of x.

  $x=7.5$ .

Given:

The given triangle.

  

Concept Used:

• If two figures or objects are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Calculation:

The given triangles are −

  

As the two triangles are similar so their corresponding sides are in equal proportion.

So $\frac{36}{30}=\frac{15}{x+5}$

  $\begin{array}{c}\frac{6}{5}=\frac{15}{x+5}\\ 6(x+5)=5(15)\\ 6x+30=75\\ 6x=75-30\\ 6x=45\\ x=\frac{45}{6}\\ x=\frac{15}{2}\\ x=7.5\end{array}$