Question

The length of a rectangle is 4 cm greater than its breadth. if the perimeter of the rectangle is 32cm what is the length and width​

Answer 1

Given :

• The length of a rectangle is 4 cm greater than its breadth. The perimeter of the rectangle is 32cm.

To Find :

• The Length and width of the rectangle.

Solution :

We know that,

$\qquad{ \bold{ \pmb{2(Length + Width) = Perimeter}}}$

So,

• Let's assume the length of the rectangle as x cm. Then the breadth will become (x – 4) cm.

Now, Substituting the given values in the formula :

$\qquad \dashrightarrow{ \sf{2[x + (x-4)] = 32}}$

$\qquad \dashrightarrow{ \sf{2(x + x-4) = 32}}$

$\qquad \dashrightarrow{ \sf{2(2x-4) = 32}}$

$\qquad \dashrightarrow{ \sf{4x-8= 32}}$

$\qquad \dashrightarrow{ \sf{4x= 32 + 8}}$

$\qquad \dashrightarrow{ \sf{4x= 40}}$

$\qquad \dashrightarrow{ \sf{x= \dfrac{40}{4} }}$

$\qquad \dashrightarrow{\pmb{ \bf{x= {10} }}}$

Therefore,

• Length = 10 cm
• Width = (10 – 4) = 6 cm

Answer 2

Given:

• The length of a rectangle is 4 cm greater than its breadth.
• Perimeter of the rectangle is 32cm

To Find:

• Length and width

Solution:

• Let Breadth of rectangle be x cm
• and Length = x + 4

Using Formula:

• Perimeter of rectangle = 2(L + B)

➞ 32cm = 2(x + x +4)

➞ 32 = 2x + 2x + 8

➞ 32 = 4x + 8

➞ 32 - 8 = 4x

➞ 24 = 4x

➞ x = 24/4

➞ x = 6cm

Therefore,

• Breadth = 6 cm
• Length = 4 + x = 10cm