Question

if the perimeter of a rectangle is 60cm and the width is half the length of the rectangle , what is the length of rectangle?​

Answer 1

Answer:

The length of rectangle is 20 cm

Answer 2

Given :

The perimeter of a rectangle is 60cm and the width is half the length of the rectangle.

To FinD :

The length of rectangle.

Solution :

Analysis :

Here the formula of perimeter of rectangle is used. We can see that the length and breadth is dependent on each other. So we have to form a equation. By using the perimeter of rectangle and equating the equation we can get the length.

Required Formula :

Perimeter of rectangle = 2(l + b)

where,

• l = length
• b = breadth

Explanation :

Let us assume that the length is "x" cm.

So, breadth is "x/2" cm.

• Perimeter = 60 cm

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

Perimeter of rectangle = 2(l + b)

where,

• l = x cm
• b = x/2 cm
• Perimeter = 60 cm

Using the required formula and substituting the required values,

⇒ Perimeter of rectangle = 2(l + b)

⇒ 60 = 2(x + x/2)

⇒ 60 = 2(2x + x/2)

⇒ 60 = 2(3x/2)

⇒ 60 = 6x/2

⇒ 60 × 2 = 6x

⇒ 120 = 6x

⇒ 120/6 = x

⇒ 20 = x

∴ x = 20 cm.

The dimensions :

1. Length = x = 20 cm
2. Breadth = x/2 = 20/2 = 10 cm

The length of the rectangle is 20 cm.

Verification :

⇒ Perimeter of rectangle = 2(l + b)

⇒ 60 = 2(20 + 10)

⇒ 60 = 2(30)

⇒ 60 = 2 × 30

⇒ 60 = 60

∴ LHS = RHS.

• Hence verified.