Question

The width of a rectangle is $10$ cm less than the length. If the perimeter of the rectangle is $80$ cm, then find the dimensions of the rectangle?

• A. $\text{length = 25 cm, width = 15 cm}$
• B. $\text{length = 30 cm, width = 20 cm}$
• C. $\text{length = 15 cm, width = 25 cm}$
• D. $\text{length = 20 cm, width = 30 cm}$

Answer 1

The correct option is A $\text{length = 25 cm, width = 15 cm}$

The perimeter $P$ of a rectangle is given by $P=2(l+w)\dots \left(i\right)$
where $l$ is the length and $w$ is the width of the rectangle.

Given, $P=80$
and the width of a rectangle is 10 centimeters less than the length
$\Rightarrow w=l-10$

Putting the values of $P$ and $w$ in equation $\left(i\right),$ we get
$80=2(l+l-10)$
$\Rightarrow 80=2(2l-10)$
Simplifying right side of the equation
$\Rightarrow 80=2\times 2l-2\times 20$
$\Rightarrow 80=4l-20$
Adding $20$ to both sides
$\Rightarrow 80+20=4l-20+20$
$\Rightarrow 100=4l$
Divide both sides by $4$
$\Rightarrow \frac{100}{4}=\frac{4l}{4}$
$\Rightarrow \frac{25\times 4}{4}=\frac{4\times l}{4}$
$\Rightarrow 25=l$
$\Rightarrow l=25$

Now, $w=l-10=25-10=15$

Hence, the length and width of the rectangle are $25$ cm and $15$ cm respectively.
Option (a.) is the correct choice.