Question

The area of a rectangle whose length is $5$ units more than twice its width is $75$ square units. What is its width?

• A. $3$ units
• B. $5$ units
• C. $7$ units
• D. $10$ units

Answer 1

The correct option is B $5$ units

Let length and width be $L$ and $B$

Given, $L=2B+5$ ....(1)
Also given $L\times B=75$ ....(2)

Substitute value of $L$ in equation (2),
$(2B+5)\times B=75$
$\Rightarrow 2B^2+5B-75=0$
$\Rightarrow 2B^2+15B-10B-75=0$
$\Rightarrow B(2B+15)-5(2B+15)=0$
$\Rightarrow (B-15)(2B+15)=0$
$\Rightarrow B=5,B=\underset{rejected}{-15/2}$
Thus $B=5$ units

Therefore, width of a rectangle is $5$ units.