Question

The area of a rectangle is $(6a^2+18a)\text{sq. units}$ and its width is $6a$. Then, its length is _____ units.

• A. 2a+3
• B. 3a+2
• C. a+3
• D. a+2

Answer 1

The correct option is C a+3

Given, area of rectangle = $6a^2+18a\text{sq. units}$
and width of the rectangle = $6a\text{units}$
We know that, area of a rectangle = length x width
Therefore,
$\text{length}\times 6a=6a^2+18a$
$⟹\text{length}=\frac{6a^2+18a}{6a}$
Here, we are dividing a polynomial by a monomial. So let's divide each term of the polynomial by the monomial.
i.e., $\frac{6a^2+18a}{6a}=\frac{6a^2}{6a}+\frac{18a}{6a}$
$=a+3$
Therefore, length of the rectangle = (a+3) units