Question

Ratio of corresponding sides of two similar triangles is 2:5,If the area of the small triangles is 64sq.cm, then what is the area of the bigger triangle? ​

Answer 1

Answer:

If two triangles are said to be similar if they have the same shape, but can be of different size. That is bigger or smaller. ΔABC

and ΔPQR

are similar.

Let area of ΔPQR=64sq.cm

. We need to find the area of ΔABC

.

“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”.

#NIKKI(≚ᄌ≚)ℒℴѵℯ❤

Answer 2

$\huge \color{lime} \boxed {\colorbox {black}{Answer}}$

We know the theorem :

The ratio of the areas of two

similar triangles is equal to the

ratio of the squares of their

corresponding sides .

Here ,

Let A1 ,A2 are areas of two similar

triangles and s1 ,s2 are their

corresponding sides respectively ,

s1 : s2 =2:5

=> s1 / s2 = 2/5 -----(1)

A1 = 64m²

A1 = ?

( s1 / s2 )² = ( A1 / A2 )

=>(2/5)²=(64/A)

=>A2

= (64×25)/4

=16×25

=400