Question

A rectangle has a length of $(5p-6)m$ and a width of $(p+4)m$. What is the width of the box, in $m$, if its perimeter is $20m$?

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (C)

$6$

Given : Rectangle length $=(5p-6)m,$ width $=(p+4)m$ and perimeter is $20m$.

We know that, perimeter of rectangle $=2(length\times breadth)$

Then perimeter of rectangle $=2\left[\right(5p-6)+(p+4\left)\right]=2(5p-6+p+4)=2(6p-2)$

But given perimeter is 20 cm

$\therefore 2(6p-2)=20$

$\Rightarrow 6p-2=10$

$\Rightarrow 6p=10+2=12$

$\Rightarrow p=2$

So width $=(p+4)=2+4=6m$