Question

If Triangle ABC similar to triangle QRP, area of triangle ABC is equals to 9 and area of triangle PQR is equals to 4,AB=18cm,BC=15cm,then find the length of PR

Answer 1

The length of the PR is equal to 10 cm.

Solution:

In triangle ABC, the area of the triangle is 9 whereas in triangle QPR the area is 4, therefore as we can see that the question says  

AB=18cm, BC=15cm, so let us find the ratio of $\frac{\ {area} \text { of } A B C}{\text {area of } Q P R}=\frac{9}{4}$

Now the ratio can be extended to $\frac{\text {area of } A B C}{\text {area of } Q P R}=\frac{9}{4}=\frac{B C^{2}}{P R^{2}}$

That means  

$\frac{B C^{2}}{P R^{2}}=\frac{9}{4}$

Now putting the value of BC = 15, we get PR  

$\frac{225}{P R^{2}}=\frac{9}{4}$

$\frac{4}{9} \times 225=P R^{2}$  

                 PR=10cm  

Therefore, the length of the PR is equal to 10 cm.