Question

Sides of two similar triangles are in the ratio 3:5. Area of these triangles are in the ratio ​

Answer 1

Answer:

The ratio of areas of these triangles → 9 : 25

Step-by-step explanation:

Concept used:

The ratio of areas of similar triangles is the square of ratio of its corresponding sides.

Mathematically,

$\boxed{\sf{\dfrac{Area \: of \: Triangle_{(1)}}{Area \: of \: Triangle_{(2)}}=\bigg(\dfrac{side_1}{side_2}\bigg)^{2}}}$

where:

Triangle₁ ~ Traingle₂

Solution:

Applying the above concept in this question,

$\sf{\dfrac{Area \: of \: Triangle_{(1)}}{Area \: of \: Triangle_{(2)}}=\bigg(\dfrac{3}{5}\bigg)^{2}}$

$\implies \sf{\dfrac{Area \: of \: Triangle_{(1)}}{Area \: of \: Traingle_{(2)}}=\dfrac{3^2}{5^2}}$

$\implies \sf{\dfrac{Area \: of \: Triangle_{(1)}}{Area \: of \: Traingle_{(2)}}=\dfrac{3 \times 3}{5 \times 5}}$

$\implies \sf{\dfrac{Area \: of \: Triangle_{(1)}}{Area \: of \: Traingle_{(2)}}=\dfrac{9}{25}}$

$\therefore \: \boxed{\boldsymbol{\sf{\dfrac{Area \: of \: Triangle_{(1)}}{Area \: of \: Traingle_{(2)}}=\dfrac{9}{25}}}}$