Question

if triangle abc is similar to triangle pqr area of triange abs =16 cm^2 and area of triangle pqr = 81 cm^2, ab =2 cm find pq

Answer 1

Answer:

$Value \:of \: PQ = \frac{8}{9}$

Step-by-step explanation:

Given ∆ABC ~ ∆PQR

Area of ∆PQR = 16 cm²,

Area of ∆ABC = 81 cm²,

AB = 2 cm,

PQ = ?

/* The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. */

$\frac{ar\:(\triangle ABC)}{ar\: (\triangle PQR)}=\left(\frac{AB}{PQ}\right)^{2}$

$\implies \frac{81}{16}=\left(\frac{2}{PQ}\right)^{2}$

$\implies \left(\frac{9}{4}\right)^{2}=\left(\frac{2}{PQ}\right)^{2}$

$\implies \frac{9}{4}=\frac{2}{PQ}$

$\implies PQ = \frac{2\times 4}{9}$

$\implies PQ = \frac{8}{9}$

Therefore,

$Value \:of \: PQ = \frac{8}{9}$

•••♪