Question

Areas of two similar traingles are 36 and 9 of traingle abc and pqr if pq is 4 then find length of ab

Answer 1

HEYA!!
----------

Given that ,

∆ ABC is similar to ∆ PQR.

Using the theorem , Ratio of Area of two Similar Triangles is equal to the ratio of square of their corresponding sides ,


$\frac{ar \: (abc)}{ar \: (pqr)} = > \frac{ab {}^{2} }{pq {}^{2} } = \frac{bc {}^{2} }{qr {}^{2} } = \frac{ac {}^{2} }{pr {}^{2} }$

$\frac{36}{9} = \frac{ab {}^{2} }{4 {}^{2} } \\ \\ ( \frac{6}{3} ) {}^{2} = ( \frac{ab}{2} ) {}^{2} \\ \\ = \frac{6}{3} = \frac{ab}{2} \\ \\ = \frac{ab}{2} = 2$
AB = 2× 2 = 4 units


-----------------------------------------------------------------------------------------------------