The lengths of corresponding sides of two similar triangles are in the ratio 5 ∶ 6. The areas of these triangles are in the ratio:

Question

Question

This question was previously asked in

RRB Group D 19 Sept 2022 Shift 1 Official Paper

Answer 1

Given:

The lengths of the corresponding sides of two similar triangles are in the ratio 5 ∶ 6

Concept used:

If two triangles are similar, then the ratio of the area of both triangles is equal to the ratio of the squares of their corresponding sides.

Calculation:

Let the similar triangles be ABC and PQR.

F1 Madhuri Railways 23.02.2023 D2

The corresponding sides of the two triangles are in the ratio AB : PQ is 5 : 6.

This means, the ratio of areas of triangles ABC and PQR will be:

\(Ar( ABC) \over Ar(PQR)\) = \(\frac{AB^2}{PQ^2}\)= \((\frac{AB}{PQ})^2\)

We already know that \(AB\over PQ\) is equal to \(5 \over 6\).

⇒ (\(5\over6\))²= \(25\over 36\)

Hence, the areas of these triangles are in the ratio 25 : 36.