Question

If the length of a rectangle is doubled, then how should breadth be altered to keep the area unchanged?

Answer 1

The area $A$ of the rectangle with length $l$ and breadth $b$ is given by, $A=\text{length}\times \text{breadth}$.

Let $l\text{'}$ be the length of the rectangle when it becomes double.

Step 1: Write $l\text{'}$ in terms of $l$.

$l\text{'}=2l$.

Step 2: Let the breadth of rectangle be $b\text{'}$. Substitute $2l$ for length , $b\text{'}$ for breadth and $l\times b$ for $A$ into the formula $A=\text{length}\times \text{breadth}$ as the area has to be same.

$l\times b=2l\times b\text{'}$

Solve the obtained equation for $b\text{'}$.

$\begin{array}{rcl}b\text{'}& =& \frac{l\times b}{2l}\\ & =& \frac{b}{2}\end{array}$

Hence, to keep the area unchanged reduce the breadth to its half.