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

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.

Answer 2

Given :-

In the two similar triangle if corresponding sides are in the ratio 9:4

To Find :-

Area in ratio

Solution :-

Here,

The square of the given sides

Squaring both sides

For Side 1

9²

81

For side 2

4²

16

Ratio = 81:16

Know More :-

Area of triangle = 1/2 × b × h

Area of rectangle = l × b

Area of square = side × side