Question

The width of a rectangle is one half its length. If the perimeter is 60 unit, find the area of rectangle

pls answer this question​

Answer 1

Given :

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

• Perimeter of the rectangle = 60 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 = 60 unit.

As We know that,

Perimeter of rectangle = 2(length + breadth)

Substituting the values in the above formula, we get,

➮ 60 = 2(x + x/2)

➮ 60 = 2(3x/2)

➮ 60 = 3x

➮ x = 60/3

➮ x = 20.

Therefore, We got the value of, x = 20.

Hence,

Length of the rectangle, x = 20 unit.

Breadth of the rectangle, x/2 = 20/2 = 10 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,

= 20 × 10

= 200.

Therefore, Area of the rectangle = 200 unit².

Answer 2

${ \huge{ \bold{ \underline{ \green{Question:-}}}}}$

▪ The width of a rectangle is one half its length. If the perimeter is 60 unit , find the area of the rectangle.

${ \huge{ \bold{ \underline{ \green{Solution:-}}}}}$

${ \bold{ \underline{ \pink{ Given-}}}}$

▪ width of the rectangle is one half its length.

▪ Perimeter of the rectangle = 60 units

${ \bold{ \underline{ \pink{To \: find-}}}}$

▪ Area of the rectangle ????

☆ Let us assume that the length of the rectangle be x units.

then , width of the rectangle

${ \bold{width = \frac{1}{2} \times length}}$

${ \bold{ \implies{width = \frac{1}{2} \times x \: units}}}$

${ \bold{ \implies{width= \frac{x}{2} units}}}$

${ \bold{ \star{ \: \: for \: rectangle}}}$

${ \boxed{ \bold{ \red{ perimeter = 2(length + width}}}}$

▪ it's given in the question that....

perimeter = 60 units

${ \bold{60 \: units = 2(x + \frac{x}{2} )}}$

${ \bold{ \implies{(x + \frac{x}{2}) = \frac{60 \: units}{2} }}}$

${ \bold{ \implies{( \frac{2x + x}{2}) = 30 \: units}}}$

${ \bold{ \implies{3x = 30 \times 2units}}}$

${ \bold{ \implies{x = \frac{30 \times 2 \: units}{3} }}}$

${ \boxed{ \bold{ \implies{ \red{x = 20 \: units}}}}}$

therefore,

▪ Length of the rectangle = x = 20 units

▪ width of the rectangle = x/2 = 20/2 = 10 units

${ \boxed{ \bold{ \red{area = length \times width}}}}$

${ \bold{area = 20units \times 10units}}$

${ \boxed{ \bold{ \implies{ \pink{area = 200 \: \: {unit}^{2} }}}}}$