## The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32 cm, then find the area of the rectangle.​

Question

The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32 cm, then find the area of the rectangle.​

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2 weeks 2021-11-22T02:00:39+00:00 2 Answers 0 views 0

55 cm^2

Step-by-step explanation:

Given:

length = l or (3b – 4)  ……….1

width = b

Therefore,

Perimeter = 2(l+b)

=> 32 = 2[(3b – 4)+b]   ………from 1

=> 32 = 2(4b – 4)

=> 32 = 2*4(b – 1)

=> 32 = 8(b – 1)

=> 32/8 = (b – 1)

=> 4 = (b – 1)

=> 4+1 = b

=> b = 5 cm

Therefore,

l = (3b – 4)

=  15 -4

=  11 cm

Therefore,

Area= l*b

=> 11 *5

=>55 cm^2

2. • The area of the rectangle is 55 square cm.

Given that:

• The length of a rectangle is 4 less than 3 times its width.
• The perimeter of a rectangle is 32 cm.

Need To Find:

• The area of the rectangle= ?

## ExPlanation:

Let x be the breadth of the rectangle.

Then, its length is (3x – 4).

Perimeter of the rectangle is 32 cm [Given]

➠ 2(l + B) = 32

Divide each side by 2.

➠ l + B = 16

Substitute (3x – 4) for l and x for B.

➠ 3x – 4 + x = 16

➠ 4x – 4 = 16

➠ 4x = 20

Divide each side by 4.

➠ x = 5

Therefore:

• Breadth of the rectangle is 5 cm.

And length of the rectangle is

➠ 3(5) – 4

➠ 15 – 4

11 cm

Formula used here:

• Area of a rectangle = Length × Breadth

Substitute 11 for l and 5 for B.

➠ 11 × 5

55

Hence:

• The area of the rectangle is 55 square cm. What is Perimeter?

• The length of the boundary of a closed figure is called the perimeter.
• Perimeter of rectangle = 2 × (Length + Breadth)
• Perimeter of a square = 4 × Side

What is Area?

• The measure of the surface enclosed by a closed figure is called area.
• Area of rectangle = Length × Breadth
• Area of a square = Side × Side 