Question

The ratio of areas of two similar right triangles is 9:16. The length of one
of the sides of the smaller triangle is 15 cm. How much longer is the length
of the corresponding side of the larger triangle from smaller triangle?​

Answer 1

Step-by-step explanation:

For similar triangles, ratio of areas = ratio of square of corresponding sides

Ar. second triangleAr. first triangle=3222

Ar.triangle64=94

Ar. of triangle  =49(64)

Ar. of triangle  =9×16

Ar. of triangle =144sq.cm

Answer 2

The side of the larger triangle is 5cm longer than that of the smaller triangle.

Given:

The ratio of the areas of two similar right triangles is 9:16.

The length of one of the sides of the smaller triangle is 15 cm.

To Find:

We need to find how much longer the length of the corresponding side of the larger triangle is than the smaller triangle.

Solution:

Let A$1$ and A$2$ be the areas of the smaller and the larger triangles respectively.

We are given that both these triangles are similar and have areas in the ratio of 9:16.

⇒ A$1$:A$2$ = 9:16.

Let S$1$ and S$2$ be the sides of the smaller and the larger triangles respectively.

We are given that S$1$ = 15cm.

From the theorem of similar triangles, we know that if two triangles are similar, then the ratio of their areas is proportional to the square of their corresponding sides, i.e.

A$1$:A$2$ = S$1$²:S$2$²

⇒ 9:16 = 15²:S$2$²

⇒ S$2$² = (15² x 16)/9 = 400.

⇒ S$2$ = 20.

Hence, the corresponding side of the larger triangle has a length of 20cm.

⇒ The side of the larger triangle is = 20-15 = 5cm longer than that of the smaller triangle.

∴The side of the larger triangle is 5cm longer than that of the smaller triangle.