Question

The areas of two similar triangles ∆ABC and ∆DEF are 144 cm² and 81 cm2 respectively. If the longest side of larger ∆ABC be 36 cm, then the longest side of the smaller triangle ∆DEF is

Options

• 20 cm

• 26 cm

• 27 cm

• 30 cm

Answer 1

Given: Areas of two similar triangles ΔABC and ΔDEF are 144cm² and 81cm².

If the longest side of larger ΔABC is 36cm

To find: the longest side of the smaller triangle ΔDEF

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

`\text{ar(Δ ABC)}/\text{ar(Δ DEF)}=(\text{longest side of larger Δ ABC}/\text{longest side of smaller Δ DEF})^2`

`114/81=(36/\text{longest side of smaller Δ DEF})^2`

Taking square root on both sides, we get

\[\frac{12}{9} = \frac{36}{\text{longest side of smaller ∆ DEF}}\]

`\text{longest side of smaller Δ DEF}=(36xx9)/12=27cm`

Hence the correct answer is `C`