Question

In the two similar triangle if corresponding sides are in the ratio 9:4 then the areas of these triangle are in the ratio​

Answer 1

Step-by-step explanation:

Given that:

In the two similar triangle,

Corresponding sides are in the ratio 9 : 4.

To Find:

The areas of these triangle are in the ratio.

Let us assume:

△ ABC ∼ △ PQR

And AB : PQ = 9 : 4

We know that:

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

i.e., Area(△ ABC) : Area(△ PQR) = (AB)² : (PQ)²

Finding the areas of these triangle are in the ratio:

⟶ Area(△ ABC) : Area(△ PQR) = (AB)² : (PQ)²

Substituting the values of AB and PQ.

⟶ Area(△ ABC) : Area(△ PQR) = (9)² : (4)²

⟶ Area(△ ABC) : Area(△ PQR) = 81 : 16

Hence,

The areas of these triangle are in the ratio is 81 : 16.