Question

if the areas of two similar triangles and triangle pqr in triangle xyz are 162 sq. Cm and 200 sq CM respectively find the ratio of their perimeters

Answer 1

Given that Δpqr is similar to Δxyz

Also given that their area is 162 cm² : 200 cm²

Formula:

$\bigg(\dfrac{Area_1}{Area_2} \bigg) = \bigg(\dfrac{length_1}{length_2} \bigg)^2$

Find the ratio:

$\bigg(\dfrac{Area_1}{Area_2} \bigg) = \bigg(\dfrac{length_1}{length_2} \bigg)^2$

$\bigg(\dfrac{length_1}{length_2} \bigg)^2 = \bigg(\dfrac{Area_1}{Area_2} \bigg)$

$\bigg(\dfrac{length_1}{length_2} \bigg)^2 = \bigg(\dfrac{162}{200} \bigg)$

$\dfrac{length_1}{length_2} = \sqrt{\dfrac{162}{200}}$

$\dfrac{length_1}{length_2} = \dfrac{9}{10}$

Answer: The ratio of their perimeter is 9 : 10