Question

The measurements of some rectangles are given in the table below. However, they are incomplete. Find the missing information.

Length	Breadth	Area	Perimeter
$20cm$	$14cm$
	$12cm$		$60cm$
$15cm$		$150cm$

• A. $280c{m}^2;68cm;18cm;216c{m}^2;10cm;50cm$.
• B. $280c{m}^2;8cm;18cm;216c{m}^2;10cm;50cm$.
• C. $20c{m}^2;68cm;18cm;216c{m}^2;10cm;50cm$.
• D. None of these

Answer 1

The correct option is A $280c{m}^2;68cm;18cm;216c{m}^2;10cm;50cm$.

Let us denote length, breadth, area and perimeter by $l,b,A,P$ respectively.

$\left(i\right)$ Given: $l=20cm,b=14cm$

Then, Area $=lb=20\times 14=280c{m}^2$

and, Perimeter $=2(l+b)=2(20+14)=68cm$

$\left(ii\right)$ Given: $b=12cm,P=60cm$

Then, $P=2(l+b)$

$\Rightarrow 60=2(l+12)$

$\Rightarrow 30=(l+12)$

$\Rightarrow l=30-12$

$\Rightarrow l=18cm$

and, Area $=lb=18\times 12=216c{m}^2$

$\left(iii\right)$ Given: $l=15cm,A=150c{m}^2$

Then, $A=lb$

$\Rightarrow 150=15b$

$\Rightarrow b=\frac{150}{15}$

$\Rightarrow b=10cm$

and, Perimeter $=2(l+b)=2(15+10)=2\times 25=50cm$

Hence, $\text{A}$ is the correct option.