Question

Perimeter of a rectangle is 1 meter. It length is 4cm less than double of its breath. Find the measure of lts length and breath

Answer 1

let breadth be x

length= 2x-4

perimeter of a rectangle = 2(l+b)

1 cm = 2 ( 2x-4+x)

1 cm =2 (3x-4)

1cm =6x-8

1cm + 8 =6x

9cm = 6x

9/6 =x

1.5 =x

length =2x-4

=2×1.5-4

=-1

breadth = x

=1.5

Answer 2

Given :

• Perimeter of the Rectangle = 1 m.

• Length of the Rectangle = 4 cm less than the double of its breadth.

To find :

• The Length and breadth of the Rectangle.

Solution :

First let us convert the perimeter of the Rectangle from m to cm.

We know that ,

1 m = 100 cm

Hence the Perimeter of the Rectangle in cm is 100 cm .

Now,

let the breadth of the Rectangle be a cm.

Hence , the length of the Rectangle will be (2a - 4) cm.

We know the formula for perimeter of a Rectangle i.e

$\bf{P = 2(l + b)}$

Where :

• P = Perimeter of the Rectangle
• l = Length of the Rectangle
• b = Breadth of the Rectangle

Using the formula for perimeter of a Rectangle and substituting the values in it , we get :

$:\implies \bf{P = 2(l + b)}$

$:\implies \bf{100 = 2(2a - 4 + a)}$

$:\implies \bf{\dfrac{100}{2} = (2a - 4 + a)}$

$:\implies \bf{50 = 2a - 4 + a}$

$:\implies \bf{50 + 4 = 2a + a}$

$:\implies \bf{54 = 2a + a}$

$:\implies \bf{54 = 3a}$

$:\implies \bf{\dfrac{54}{3} = a}$

$:\implies \bf{a = 18}$

$\boxed{\therefore \bf{a = 18}}$

Hence, the value of a is 18 cm.

• Breadth = a = 18 cm

• Length = 2a - 4 = 2(18) - 4 = 36 - 4 = 32 cm.

Hence the length of the Rectangle is 32 cm and the breadth of the Rectangle is 18 cm.