Question

The areas of two similar triangles $ABC$and$DEF$ are $144c{m}^2$ and $81c{m}^2,$respectively. If the longest side of larger triangle $ABC$ is $36cm$, then the longest side of the smaller triangle $DEF$ is

• A. $20cm$
• B. $26cm$
• C. $27cm$
• D. $30cm$

Answer 1

The correct option is C

$27cm$

Explanation for the correct option:

Ratios of area of similiar triangles:

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

$ar△ABC$$=144c{m}^2$

$ar△DEF=$$81c{m}^2,$

Ratio of areas$=144:81$

We know that,

Ratio of areas of two similar triangles is equal to the ratio of square of their corresponding sides.

Thus,

$\begin{array}{rcl}\frac{ar△ABC}{ar△DEF}& =& \frac{144}{81}\\ & =& \frac{{12}^2}{9^2}\end{array}$

Ratio of sides $=12:9$

Let the longest side of similiar triangle$DEF$ be $X$

Then

$36:X=12:9$

$$\begin{gathered} \frac{36}{X}=\frac{12}{9} \\ \Rightarrow 36\times 9=12X \\ \Rightarrow X=\frac{36\times 9}{12} \\ =27cm \end{gathered}$$

Hence, the longest side of the smaller triangle $DEF$ is $27cm$

Hence, the correct option is (C)