Question

Find the ratio of the areas of two similar triangles if two of their corresponding sides are of length 3 cm and 5 cm

Answer 1

Answer:

$\large{\underline{\boxed{\sf 9:25}}}$

Step-by-step explanation:

We know that ;

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

That is,

$\rm \dfrac{Area \: 1}{Area \: 2}= \left(\dfrac{Length \: 1}{Length \: 2}\right)^2$

Given that,

Length of two corresponding sides are 3 cm and 5 cm.

Ratio of length = 3 : 5

$\rm \dfrac{Area \: 1}{Area \: 2}=\left(\dfrac{3}{5}\right)^2$

⇒ $\rm \dfrac{Area \: 1}{Area \: 2}= \dfrac{9}{25}$

Hence, the ratio of the areas of two similar triangles is 9 : 25.

Answer 2

Answer : 9 : 25

Step by step explanation :

We know that,

The ratio of areas of two similar triangles is equal to the square of ratio of their corresponding sides.

Side1 = 3 cm, Side2 = 5 cm.

Thus,

$\tt{ \frac{Area \: of \triangle1}{Area \: of \triangle2} = \frac{(side1) {}^{2} }{(side2) {}^{2} }}$

$\tt{ = \frac{(3) {}^{2} }{(5) {}^{2} }}$

$\tt{{ \implies \frac{9}{25} } = 9 \ratio25}$

Thus,

The ratio of areas of two triangles is 9 : 25.