Question

g. The perimeter of a rectangle is 48 cm. If the length is double of its breadth, find
its length, breadth and area.​

Answer 1

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Let breadth of the rectangle be 'b' cm.

So length of the rectangle will be 'b+2' cm.

Now

Perimeter =48

2(l+b)=48

2(b+2+b)=48

2b+2=24

2b=22

b=11 cm

l=b+2

=13 cm

Then,

Area of the rectangle =l×b

=13×11

=143 cm²

Answer 2

Answer :

›»› The length and breadth of a rectangle is 8 cm and 16 cm respectively.

›»› The area of a rectangle is 128 cm².

Step-by-step explanation :

Given :

• Perimeter of a rectangle = 48 cm.
• The length is double if its breadth.

To Find :

• Length and breadth of a rectangle = ?
• Area of rectangle = ?

Formula required :

Formula of perimeter of rectangle to calculate the length and breadth of rectangle is given by,

→ Perimeter of rectangle = 2(l + b).

Here,

• l is the length of rectangle.
• b is the breadth of rectangle.

Units,

• The unit of length is cm.
• The unit of breadth is cm.

Formula to calculate the area of rectangle is given by,

→ Area of rectangle = l × b.

Here,

• l is the length of rectangle.
• b is the breadth of rectangle.

Units,

• The unit of length is cm.
• The unit of breadth is cm.

Solution :

Let us consider that, breadth of a rectangle is x cm.

As it is given that, the the length is double of its breadth.

→ Length = 2x cm.

According to the given question,

As we are given with the perimeter of rectangle length and breadth of rectangle in a variable so we know the required formula, that is,

→ Perimeter of rectangle = 2(l + b).

By using the formula of perimeter of rectangle to calculate the length and breadth of rectangle and substituting all the given values in the formula, we get :

→ 48 = 2{(2x) + (x)}

→ 48 = 2(2x + x)

→ 48 = 2 × 3x

→ 48 = 6x

→ x = 48/6

→ x = 8.

Therefore,

The length and the breadth of a rectangle will be,

• Length, x = 8 cm.
• Breadth, 2x = 2 × 8 = 16 cm.

Hence, the length and the breadth of a rectangle is 8 cm and 16 cm respectively.

Now,

We know that, if we are given with length of rectangle and breadth of rectangle then we have the required formula, that is,

→ Area of rectangle = l × b.

By using the formula to calculate the area of rectangle and substituting all the given values in the formula, we get :

→ Area of rectangle = 8 × 16

→ Area of rectangle = 128.

Hence, the area of a rectangle is 128 cm².