Question

The perimeters of two similar triangles abc and pqr are 35 cm and 45 cm hen the ratio of the areas of the two triangles is

Answer 1

Step-by-step explanation:

$\frac{perimeter \: of \: abc}{perimeter \: of \: pqr} = \frac{35}{45} = \frac{7}{9}$

Since the ratio of square of perimeters of similar triangles is equal to the ratio of their corresponding areas.

therefore

Required ratio

=

$\frac{ {7}^{2} }{ {9}^{2} } = \frac{49}{81}$

Answer 2

The ratio of the areas of the two triangles is 49:81.

Explanation:

• The ratio of perimeter of two similar triangles is equal to the ratio of their corresponding sides. (1)
• The ratio of the area of two similar triangle is equal to the ratio of the square of the corresponding sides. (2)

From (1) and (2) , we have

The ratio of the area of two similar triangle is equal to the ratio of the square of their perimeters.

Given : The perimeters of two similar triangles ΔABC and ΔPQR are 35 cm and 45 cm.

Then, the  ratio of the areas of the two triangles would become

$\dfrac{\text{Area of }\triangle ABC}{\text{Area of }\triangle PQR}=\dfrac{(\text{Perimeter of }\triangle ABC)^2}{(\text{Perimeter of }\triangle PQR)^2}$

i.e. $\dfrac{\text{Area of }\triangle ABC}{\text{Area of }\triangle PQR}=\dfrac{(35)^2}{(45)^2}$

i.e. $\dfrac{\text{Area of }\triangle ABC}{\text{Area of }\triangle PQR}=\dfrac{(5\times7)^2}{(5\times9)^2}$

i.e. $\dfrac{\text{Area of }\triangle ABC}{\text{Area of }\triangle PQR}=\dfrac{(5)^2(7)^2}{(5)^2(9)^2}$

i.e. $\dfrac{\text{Area of }\triangle ABC}{\text{Area of }\triangle PQR}=\dfrac{(7)^2}{(9)^2}=\dfrac{49}{81}$

∴ The ratio of the areas of the two triangles is 49:81.

# Learn more : Similar triangles and congurent triangles

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