Question

Ratio of the corresponding sides of two similar triangles is 2:5, if the area of the smaller triangle is 16 sq.cm, What is the area of the bigger triangle? ​

Answer 1

Step-by-step explanation:

The ratio of the areas of two similar triangles is equal to the square of ratio of their corresponding sides”. That is area of ΔPQRarea ofΔABC=(PQAB)2

----- (1)

But, the ratio between the corresponding sides of two triangles are given.

That is, PQAB=25

. Substituting this in (1).

⇒64area ofΔABC=(25)2

⇒64area ofΔABC=(425)

Cross multiplying and rearranging the equation,

⇒area ofΔABC64=254

⇒area ofΔABC=64×254

⇒area ofΔABC=16004

⇒area ofΔABC=400sq.cm

Hence, the area of ΔABC

is 400 sq.cm

So, the correct answer is “400 sq.cm”.