Question

What is the length and breadth of a rectangle if its perimeter is 12 cm and its length is 2 times its breadth?

• A. 4 cm, 2 cm
• B. 2 cm, 1 cm
• C. 6 cm, 3 cm
• D. 7 cm, 4 cm

Answer 1

The correct option is A 4 cm, 2 cm

Given that,
$length=2\times breadth$
$l=2b$

We know that,
opposite sides of the rectangle are of equal length.

Perimeter of the rectangle
= Length of side AB + Length of side BC + Length of side CD + Length of side DA
= $l+b+l+b$
= $2l+2b$
=$2(l+b)$
=$2(2b+b)$ = $2\left(3b\right)$= $6b$

Now, perimeter of the rectangle = 12 cm

So, $6b=12cm$

Using $trialanderrormethod$,

case 1:

putting $b=1$,
LHS = $6\times 1$ = 6
Hence, LHS is not equal to RHS.

case 2:

putting $b=2$,
LHS = $6\times 2$ = 12
Hence, LHS is equal to RHS.

$\therefore$ $breadth=2cm$
$length=2\times breadth$
$length=2\times 2$ = 4 cm