Question

The perimeter of a rectangle is 24 cm and its area is 32 sq. cm. Find the length of the longer side.

• A. 8 cm
• B. 16 cm
• C. 12 cm
• D. 4 cm

Answer 1

The correct option is A

8 cm

Let the length of the rectangle be $x$ cm.

Perimeter = 24 cm

$\Rightarrow$ length + breadth = 12 cm
[Perimeter of a rectangle = 2 (l + b)]

Therefore breadth = $12-x$ cm

Area = 32 sq. cm

$\Rightarrow$ $(12-x)\left(x\right)=32$

$\Rightarrow$ $12x-x^2=32$

$\Rightarrow$ $x^2-12x+32=0$

$\Rightarrow$ $x^2-8x-4x+32=0$

$\Rightarrow$ $x(x-8)-4(x-8)=0$

$\Rightarrow$ $(x-8)(x-4)=0$

$\Rightarrow$ $x=8,4$

If x = 8 cm then length = 8 cm and breadth = 12 - 8 = 4 cm.

Similarly, if x = 4 cm, length = 4 cm and breadth = 12 - 4 = 8 cm.

Either way length of the longer side will be 8 cm.