Question

A rectangular field has a length $10$ feet more than it is width. If the area of the field is $264$, what is the width of the rectangular field?

• A. $26$
• B. $12$
• C. $9$
• D. $4$

Answer 1

The correct option is B $12$

Let width of rectangular field be $x$ feet.

Then length of a rectangular field becomes $(x+10)$ feet.

$\Rightarrow$ Area of rectangular field $=264$

$\Rightarrow$ $x\times (x+10)=264$

$\Rightarrow$ $x^2+10x=264$

$\Rightarrow$ $x^2+10x-264=0$

$\Rightarrow$ $x^2+22x-12x-264=0$

$\Rightarrow$ $x(x+22)-12(x+22)=0$

$\Rightarrow$ $(x+22)(x-12)=0$

$\Rightarrow$ $x+22=0$ or $x-12=0$

$\Rightarrow$ $x=-22$ or $x=12$

Length cannot be negative, so $x=-22$ is not possible.

$\therefore$ $x=12$

$\therefore$ Width of rectangular field is $12$ feet.