Question

(ii) Each question carries 2 mark.
The perimeters of two similar triangles are 12 cm and 72 cm. If the area of
smaller triangle is 6 cm, find the area of bigger triangle.​

Answer 1

Answer:

216 cm square

Step-by-step explanation:

as we know theorems that

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

and the ratio of the sides of triangles is equal to the ratio of their corresponding perimeters.

hence,

the ratio of the areas of the triangles will be equal to the square of the ratio of their corresponding perimeters .

so,

assuming area of larger triangle x cm squares

(12 / 72)^2= 6 / x

( 1 / 6) ^2 = 6 / x

1 / 36 = 6/x

x = 216 cm^2

hence, the area of larger triangle will be 216 square cm.

Answer 2

Answer :-

216 cm²

Solution :-

Perimeter of one of the similar triangle i.e smaller triangle = 12 cm

Perimeter of another similar triangle i.e bigger triangle = 72 cm

Area of smaller triangle = 6 cm²

Let the area of bigger triangle be x cm²

We know that

Ratio of areas of similar triangles = Ratio of squares of perimeters of corresponding triangles

⇒ ar( bigger Δ ) / ar(smaller Δ ) = ( Perimeter of bigger Δ )² / ( Perimeter of smaller Δ )²

⇒ x / 6 = ( 72 )² / ( 12 )²

⇒ x / 6 = ( 72 / 12 )²

⇒ x / 6 = 6²

⇒ x = 36 * 6

⇒ x = 216

Therefore, the area of bigger triangle is 216 cm².