Question

The perimeter of a square is 48 cm . The area of a rectangle is 4 cm2 less than the area of the square . If length of the rectangle is 14 cm , then its perimeter is

Answer 1

perimeter of square = 48cm

side of square = 48/4 = 12cm

area of square = side x side = 12^2 = 144 sq.cm

area of rectangle = area of square - 4 sq cm = 144 - 4 = 140 sq.cm

length = 14 cm

so, breadth = area/length = 140/14 = 10 cm

So, perimeter = 2(10 + 14) = 2(24) = 48 cm

Answer 2

Given:

The perimeter of a square is 48 cm. The area of a rectangle is 4 cm2 less than the area of the square and the length of the rectangle is 14 cm.

To find:

The perimeter of a rectangle.

Solution:

As given,

The perimeter of a square = 48 cm.

So,

The side of the square

$= \frac{48}{4}$

$= 12 \: cm$

(as the perimeter of a square = 4 × length of a side)

Now,

The area of a given square

$= {(side)}^{2}$

$= {(12)}^{2}$

$= 144 \: {cm}^{2}$

Now,

length 'l' of a rectangle = 14 cm

the area of a rectangle

$= area \: of \: the \: square \: - \: 4 {cm}^{2}$

$= (144 - 4) {cm}^{2}$

$= 140 {cm}^{2}$

Also,

Area of rectangle

$= \: length \: of \: rectangle \: \times breadth \: of \: rectangle$

$= 14 \times breadth$

Now,

$14 \times breadth = 140$

So,

$breadth \: = \frac{140}{14}$

$= 10 \: cm$

So,

the perimeter of a rectangle

$= 2(length \: + \: breadth)$

$= 2(10 + 14)$

$= 2(24)$

$= 48 \: {cm}$

Hence, the perimeter of a rectangle is 48 cm.