Question

The width of a rectangle is one half its length. If the perimeter is 90 unit, find the area of rectangle.

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Answer 1

Given :

• The width of a rectangle is one half its length.

• Perimeter of the rectangle = 90 unit.

To find

• The Area of Rectangle =?

Step-by-step explanation :

Let, the length of the rectangle be x.

Then, the width of the rectangle be, x × 1/2 = x/2

It is Given that,

Perimeter of the rectangle = 90 unit.

As We know that,

Perimeter of rectangle = 2(length + breadth)

Substituting the values in the above formula, we get,

➮ 90 = 2(x + x/2)

➮ 90 = 2(3x/2)

➮ 90 = 3x

➮ x = 90/3

➮ x = 30.

Therefore, We got the value of, x = 30.

Hence,

Length of the rectangle, x = 30 unit.

Breadth of the rectangle, x/2 = 30/2 = 15 unit.

Now,

We have to find the Area of the rectangle,

As We know that,

Area of Rectangle = length x breadth

Substituting the values in the above formula, we get,

= 30 × 15

= 450.

Therefore, Area of the rectangle = 450 unit².

Answer 2

Given :-

• Width of the reactangle is one half its length.

• Perimeter of reactangle is 90 units.

To find :-

The area of reactangle.

Answer :-

Let the length of reactangle be the x units.

then, width of the reactangle = 1/2 × length

➧ width = 1/2 × x units

➧ width = x/2 units

Perimeter of the reactangle = 90 units (Given)

Perimeter of reactangle = 2 ( length + Breadth )

➧ 90 units = 2 (x + x/2)

➧ x + x/2 = 90/2

➧ 2x + x/2 = 45

➧ 3x = 45 × 2

➧ x = 90/2

➧ x = 30 units

Therefore,

• the length of the reactangle = x = 30 units

• Width of the reactangle = x/2 = 30/2 = 15 units

Area = length × Breadth

➧ Area = 30 units × 15 units

➧ Area = 450 unit²

Therefore, the area of reactangle is 450 unit².