Question

The areas of two similar ∆ABC and ∆DEF are 225 cm² and 81 cm² respectively. If the longest side of the larger triangle ∆ ABC be 30 cm, find the longest side of the smaller triangle DEF.

Answer 1

Two Triangles are said to be similar if their i)corresponding angles are equal and ii)corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal)

SOLUTION:

GIVEN:
ar(∆ABC) / ar(∆DEF) = 225/81 cm²
Side of a larger ∆ABC = 30 cm

ar(larger ∆ABC ) / ar(Smaller ∆DEF ) = (Side of a larger ∆ / Side of a Smaller ∆)²

[The ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides]

225 / 81 = (30 /Side of a Smaller ∆)²

Taking square root on both sides

15 / 9 = 30 /Side of a Smaller ∆
15 × Side of a Smaller ∆ = 30 × 9
Side of a Smaller ∆ = (30 × 9)/15
Side of a Smaller ∆ = 2× 9
Side of a Smaller ∆ = 18 cm

Hence, the the longest side of the smaller ∆ DEF is 18 cm

HOPE THIS WILL HELP YOU...

Answer 2

Given : ar (∆ABC)/ ar (∆DEF) = 225 / 81-----(i)

Let the Longest Side in both triangles be AB and DE.

We know that, The ratio of areas of two Similar Triangles is equal to the ratio of the square of their corresponding sides.

So, ar (∆ABC) / ar (∆DEF) = (AB / DE)²------(ii)

From (i) and (ii)

(AB / DE)² = 225 / 81
(AB / DE) = √225 / 81
30 / DE = 15 / 9
DE = 30 x 9/15
DE = 2 x 9
DE = 18cm

∴, The Longest Side in ∆DEF is 18cm i.e, DE = 18cm.