Question

The area of a rectangle is $(a^4+a^2+1)$ sq. units and its length is $(a^2-a+1)$units ,find its breadth?

Answer 1

Area of a rectangle $=(a^4+a^2+1)$ sq.units

Length $=(a^2-a+1)$

Area of rectangle = Length $\times$ Breadth

$a^4+a^2+1=(a^2-a+1)\times$ Breadth

Breadth $=\frac{a^4+a^2+1}{a^2-a+1}$

$a^4+a^2+1={\left(a^2\right)}^2+2.a^2.1+1-a^2$

$={(a^2+1)}^2-a^2$

$=(a^2+1-a)(a^2+1+a)$

$\therefore$ Breadth $=\frac{(a^2+a+1)(a^2-a+1)}{(a^2-a+1)}$

$=(a^2+a+1)$