Question

The length of a rectangle is three times it's width the perimeter of the rectangle is 24 cm calculate the area of the rectangle

Answer 1

Answer : 27 cm²

$\rule{100}2$

Given :

• Length =  3 × breadth
• Perimeter = 24 cm

To Find :

• Area of rectangle

Solution :

Let width of the rectangle be ' x '

So, length will be ' 3x '

Also, It is given that it's perimeter is 24 cm.

We know that,

$\sf Perimeter\:of\:Rectangle= 2(length+breadth)$

Substitute the given values in order to find length & breadth of the rectangle.

We get,

$\sf 24 = 2 ( 3x + x )$

$\sf\implies 24 = 2 (4x)$

$\sf\implies 24 = 8x$

$\sf\implies x =\dfrac{24}{8}$

$\sf\therefore x = 3$

Hence,

Width of the given rectangle is 3 cm

Length will be ⇒ 3 × 3 = 9 cm

Finally,

$\sf Area\:of\:Rectangle=length\times breadth$

$\sf = 9\times 3$

$\sf = 27 cm^2$

Therefore,

Area of the given rectangle is 27 cm².

$\rule{200}2$

Answer 2

$\mathtt{ \huge{ \fbox{Solution :)}}}$

Given ,

• The length of a rectangle is three times it's width
• Perimeter of rectangle = 24 cm

Let , width of rectangle be x

Then , length of rectangle = 3x

We know that , the perimeter of rectangle is given by

$\large \mathtt{ \fbox{Perimeter =2(l + b)}}$

Thus ,

24 = 2(3x + x)

24 = 2(4x)

24 = 8x

x = 24/8

x = 3 cm

Hence , length and width of the rectangle are 9 cm and 3 cm

We know that , the area of rectangle is given by

$\large \mathtt{ \fbox{Area = l \times b}}$

Substitute the known values , we get

Area = 9 × 3

Area = 27 cm²

Hence , the area of rectangle is 27 cm³

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