Question

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

Answer 1

Answer:

Let the width be xcm, then,

The length = 3x -4cm

A/Q

2 X (3x - 4 + x) = 32 cm

=> 2 X (4x - 4) = 32 cm

=> 8x - 8 =32

=> 8x = 32 + 8

=> 8x = 40

=> x = 40/8

=> x = 5

Width = x cm

           = 5 cm

Length = 3x - 4

            = 15 - 4

            = 11 cm

Area = l X b

        = 11 cm X 5 cm

       = 55 cm²

Thus, the area of the rectangle is 55 cm²

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Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

AnswEr:

• 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

Add 4 top each side.

➠ 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.

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Additional Information:

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

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