Question

The area of a rectangle is given by the expression $p(4p^2-16)$. If the length of the rectangle is $4p(p-2)$, then find the expression for the breadth of the rectangle.

Answer 1

Given, area of the rectangle = $p(4p^2-16)$ sq. units
Length of the rectangle = $4p(p-2)$ units

Area of rectangle = length x breadth

$\Rightarrow p(4p^2-16)=4p(p-2)\times breadth$

$\Rightarrow \text{breadth}=\frac{p(4p^2-16)}{4p(p-2)}$

$\Rightarrow \text{breadth}=\frac{(4p^2-16)}{4(p-2)}$

$\Rightarrow \text{breadth}=\frac{(2p{)}^2-4^2}{4(p-2)}$

We know, $a^2-b^2=(a+b)(a-b)$

$\Rightarrow \text{breadth}=\frac{(2p-4)(2p+4)}{4(p-2)}$

$\Rightarrow \text{breadth}=\frac{2(p-2)\times 2(p+2)}{4(p-2)}$

$\Rightarrow \text{breadth}=\frac{4(p-2)(p+2)}{4(p-2)}$

$\Rightarrow \text{breadth}=(p+2)\text{units}$