Question

The side of two triangles are 4:9 what is the ratio of their area ?​

Answer 1

Complete step-by-step answer:

It is given that, Sides of two similar triangles are in ratio

4:9.

Let, AABC and ADEF are the two given similar

triangles.

We need to find the ratio of

Area (AABC): Area(ADEF).

Thus we have their sides in the ratio 4: 9. → AB : DE = AC: DF = BC: EF = 4:9.... (1)

We know that if two triangle are similar, Ratio of areas is equal to square of ratio of its corresponding sides

⇒ Area (AABC): Area(ADEF) = (BC: EF)2

Putting the values in (1)

→ Area (A ABC) : Area(A DEF) = (4:9)² = 16::

Hence, the areas of triangles AABC and ADEF is:

16: 81.

Hence, when sides of two similar triangles are in ratio

4:9. Areas of these triangles are in the ratio: 16: 81.

Answer 2

If two triangles are similar to each other, then the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides of these triangles.

and the ratio of given sides are 4:9

so, the ratio of their areas will be like

= (4)² : (9)²

= 16:81