Question

The length of a rectangle is four times its breadth. Find the simplified expression for the perimeter and the area of the rectangle.
( $l$ = Length of the triangle, $b$ = Breadth of the triangle)

• A. Perimeter $=5b$ units
  Area $=4b^2$ square units
• B. Perimeter $=10b$ units
  Area $=5b^2$ square units
• C. Perimeter $=10b$ units
  Area $=4b^2$ square units
• D. Perimeter $=4b^2$ units
  Area $=10b$ square units

Answer 1

The correct option is C Perimeter $=10b$ units

Area $=4b^2$ square units
$\underset{–}{\text{Given:}}$
$l=$ Length of the rectangle
$b=$ Breadth of the rectangle

Now, according to the question length $\left(l\right)$ is $4$ times the breadth $\left(b\right)$ of the rectangle. Which means,
$l=4\times b$
$\Rightarrow l=4b$

Perimeter of the rectangle
$=2(l+b)$

$=2(4b+b)$ $[\because l=4b]$

$=2\times 5b=10b$

$\therefore$ Perimeter of the rectangle is $\underset{–}{10b}$ units.

Area of the rectangle
$=l\times b$

$=4b\times b$ $[\because l=4b]$


$=4b^{(1+1)}$ $[\because a^m\times a^n=a^{(m+n)}]$

$=4b^2$

$\therefore$ Area of the rectangle is $\underset{–}{4b^2}$ square units.

Therefore, option (c.) is the correct answer.