Question

The length and breadth of a rectange are in the ratio 2:1 .If its perimeter is 60 cm then find it's length and breadth​

Answer 1

Given :

• The length and breadth of a rectange are in the ratio 2:1.
• Its perimeter is 60 cm.

To Find :

The length and breadth.

Solution :

Analysis :

Here the concept of perimeter of rectangle is used. We have to take common ratios. After that using the formula of perimeter of rectangle we will form a equation. Then equating the equation we can find the length and the breadth.

Required Formula :

• Perimeter of rectangle = 2(l + b)

where,

• l = Length
• b = Breadth

Explanation :

Let the common ratio be “x”.

• Length = 2x
• Breadth = x

• Perimeter = 60 cm

We know that if we are given the ratio of length and breadth and the perimeter and is asked to find the length and breadth then our required formula is,

Perimeter of rectangle = 2(l + b)

where,

• Perimeter = 60 cm
• l = 2x
• b = x

Using the required formula and substituting the required values,

⇒ Perimeter = 2(l + b)

⇒ 60 = 2(2x + x)

⇒ 60 = 4x + 2x

⇒ 60 = 6x

⇒ 60/6 = x

⇒ 10 = x

∴ x = 10.

The dimensions :

• Length = 2x = 2 × 10 = 20 cm
• Breadth = x = 10 cm

The length and breadth is 20 cm & 10 cm respectively.

Verification :

LHS = 60 cm.

RHS :

2(l + b)

• Putting l = 20 & b = 10;

⇒ 2(20 + 10)

⇒ 2 × 30

⇒ 60

RHS = 60 cm.

∴ RHS = LHS.

• Hence verified.