Question

perimeter of two similar triangles are 12 cm and 72 cm . if the area of smaller triangle is 6 cm² . find the area of bigger triangle​

Answer 1

Answer:

The area of the bigger triangle will be 36 cm^2.

Step-by-step explanation:

12/72 = 6/x

12x = 432

x = 432/12

x = 36 cm^2.

Answer 2

The area of the bigger triangle is $216\ cm^2$ .

Explanation:

We know that the ratio of the perimeter of two similar triangles is equal to the ratio of their corresponding sides .    (1)

According to a theorem ,

The ratio of the area of two similar triangles 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 triangles is equal to the ratio of the square of their corresponding perimeter.      (3)

Given : Perimeter of two similar triangles are 12 cm and 72 cm .

If the area of smaller triangle is 6 cm², then by (3), we have

$\dfrac{\text{Area of bigger triangle}}{\text{Area of smaller triangle}}=\dfrac{(\text{Perimeter of bigger triangle})^2}{(\text{Perimeter of smaller triangle})^2}\\\\\Rightarrow\ \dfrac{\text{Area of bigger triangle}}{6}=\dfrac{(72)^2}{12^2}\\\\\Rightarrow\ \text{Area of bigger triangle}=\dfrac{72\times72}{12\times12}\times6\\\\\Rightarrow\ \text{Area of bigger triangle}=216\ cm^2$

Hence, the area of the bigger triangle is $216\ cm^2$ .

# Learn more :

The areas of two similar triangles are 81 cm square and 49 CM square respectively if the altitude of bigger triangle is 4.5 cm find the corresponding attitude of the smaller triangles​

https://brainly.in/question/11631871