Question

If each side of a rhombus is doubled, how much will its area increase?

• A. $1.5$ times
• B. $2$ times
• C. $3$ times
• D. $4$ times

Answer 1

The correct option is D

$4$ times

Explanation for the correct option:

Area of a rhombus is given as $A=bh$

Where, $b$ is the base and $h$ is the height.

Initially, the area will be, $A_1=bh$

When all the sides are doubled, base and height also get doubled.

Thus, $b$ becomes $2b$ and $h$ becomes $2h$.

Then the new area is,

$\begin{array}{rcl}& & \begin{array}{cc}& A_2=2b\times 2h\\ & =4bh\\ \Rightarrow & A_2=4A_1\end{array}\end{array}$

Therefore, the area increases $4$ times when the sides of a rhombus are doubled.

Hence, option D is correct.