Question

given triangle ABC SIMILAR TO triangle PQR if AB/PQ =1/3 then find area ABC/PQR

Answer 1

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Answer 2

Answer:

$\frac{Area \:of \: Triangle\:ABC}{Area \:of \: Triangle\:PQR}\\=\frac{1}{9}$

Step-by-step explanation:

Given:

∆ABC~∆PQR

$\frac{AB}{PQ}=\frac{1}{3}$

To Find:

Ratio of Area ∆ABC and ∆PQR.

Solution:

/* By Theorem:

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

Here,

$\frac{Area \:of \: Triangle\:ABC}{Area \:of \: Triangle\:PQR}\\=\frac{AB^{2}}{PQ^{2}}\\=\big(\frac{AB}{PQ}\big)^{2}\\=\big(\frac{1}{3}\big)^{2}\\=\frac{1}{9}$

Therefore,

$\frac{Area \:of \: Triangle\:ABC}{Area \:of \: Triangle\:PQR}\\=\frac{1}{9}$

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