Question

the length of a rectangle is 3 m less than two times with. if perimeter of rectangle is 120 m. Find its dimensions.​

Answer 1

Required Answer :

The dimensions of the rectangle are :-

• Length = 39 m
• Breadth = 21 m

Given :

• Length of the rectangle is 3 m less than two times the width
• Perimeter of the rectangle = 120 m

To find :

• Dimensions of the rectangle

Concept :

To calculate the dimensions of the rectangle, i.e. the length and breadth of the rectangle. Firstly, we will assume them according to the condition given in the question. Then by using the formula of periemter of rectangle we will find the dimensions.

Perimeter is the sum of all the sides.

Mathematically,

• Perimeter = 2(l + b)

where,

• l denotes the length
• b denotes the breadth

Solution :

Let,

⇒ Breadth of the rectangle = x metre

⇒ Length of the rectangle = 2(Breadth) - 3

⇒ Length of the rectangle = 2x - 3 metre

Using formula,

• Perimeter = 2(l + b)

Substituting the given values :-

⇒ 120 = 2(2x - 3 + x)

⇒ 120 = 2(3x - 3)

⇒ 120/2 = 3x - 3

⇒ 60 = 3x - 3

⇒ 60 + 3 = 3x

⇒ 63 = 3x

⇒ 63/3 = x

⇒ 21 = x

The value of x = 21

Substituting the value of 'x' in the dimensions of rectangle which we've assumed :-

LENGTH :-

⠀⠀⠀⇒ Length of the rectangle = 2x - 3

⠀⠀⠀⇒ Length of the rectangle = 2(21) - 3

⠀⠀⠀⇒ Length of the rectangle = 42 - 3

⠀⠀⠀⇒ Length of the rectangle = 39 m

BREADTH :-

⠀⠀⠀⇒ Breadth of the rectangle = x

⠀⠀⠀⇒ Breadth of the rectangle = 21 m