Question

The areas of two similar triangles $\Delta ABC$ and $\Delta DEF$ are $144c{m}^2$ and $81c{m}^2$ respectively. If the longest side of larger $\Delta ABC$ be $36cm$, then the longest side of the smaller triangle $\Delta DEF$ is
(a) $20cm$
(b) $26cm$
(c) $27cm$
(d) $30cm$

Answer 1

The correct option is C: $27cm$

Given: Areas of two similar triangles $\Delta ABC$ and $\Delta DEF$ are $144c{m}^2$ and $81c{m}^2.$

If the longest side of larger $\Delta ABC$ is $36cm.$

To find: the longest side of the smaller triangle $\Delta DEF$

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

$\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta DEF\right)}=$ $[\frac{\text{longest side of larger}\Delta ABC}{\text{longest side of smaller}\Delta DEF}{]}^2$

$or,\frac{144}{81}$ $=$ $[\frac{36}{\text{longest side of smaller}\Delta DEF}{]}^2$

Taking square root on both sides, we get

$\Rightarrow \frac{12}{9}=\frac{36}{\text{longest side of smaller}\Delta DEF}$

$\therefore \text{longest side of smaller}\Delta DEF=\frac{36\times 9}{12}=27cm$

Hence the correct answer is C.