Question

the area of a rectangle is 21cm square.if one side exceeds the other by 4 cm.find the dimensions of the rectangle.

Answer 1

the Length is 7 cm
and Breadth is 3 cm
that implies 7 x 3 = 21 cm^2

Answer 2

Given:

The area of a rectangle is 21cm Square and one side exceeds the other by 4 cm.

To find:

The dimensions of the rectangle.

Solution:

As we know that the area of a rectangle having length 'l' and breadth 'b' is given by using the formula:

$area \: = l \times b$

Now,

as given

The area of the rectangle = 21cm square.

Let one side of the rectangle be x cm.

So,

the other side of the rectangle = (x + 4) cm

Thus,

$21 = (x)(x + 4)$

${x}^{2} + 4x - 21 = 0$

This can be written as

${x}^{2} + 7x - 3x - 21$

$x(x + 7) - 3(x + 7)$

$(x - 3)(x + 7)$

When

x - 3 = 0 and x + 7 = 0

x = 3, -7

Neglecting x = -7 as a side cannot be negative.

So,

One side of rectangle = 3m

Another side of the rectangle = 3 + 4 = 7m

Hence, the dimensions of the rectangle are 3m and 7m.