Question

The width of the rectangle is 2/3 of its length. If the perimeter of the rectangle is 80 cm. Find the dimensions of the rectangle and also find its area.

Answer 1

Step-by-step explanation:

Given :-

The width of the rectangle is 2/3 of its length. The perimeter of the rectangle is 80 cm.

To find :-

1) The dimensions of the rectangle

2) It's area

Solution :-

Let the length of the rectangle be X cm

Then, the width of the rectangle

= 2/3rd of it's length

= 2/3 of X

= (2/3)×X

= (2×X)/3

= 2X/3

Width of the rectangle = 2X/3 cm

We know that

Perimeter of a rectangle = 2(length+width) units

Perimeter of the given rectangle

=> P = 2[X+(2X/3)] cm

=> P = 2[(3X+2X)/3] cm

=> P = 2(5X/3) cm

=> P = 10X/3 cm

According to the given problem

Perimeter of the rectangle = 80 cm

Therefore, 10X/3 = 80

=> 10X = 80×3

=> 10X = 240

=> X = 240/10

=> X = 24

If X = 24 then Length = X cm = 24 cm

If X = 24 then Width = 2X/3 cm

=> Width = 2×24/3

=> Width = 2×8

Therefore, Width= 16 cm

We know that

Area of a rectangle = length×width sq.units

Area of the given rectangle = 24×16 cm²

Therefore, Area = 384 cm²

Answer :-

1) The dimensions of the rectangle are 24 cm and 16 cm

2) Area of the rectangle = 384 cm²

Used formulae:-

→ Perimeter of a rectangle = 2(length+width) units

→ Area of a rectangle = length×width sq.units

Answer 2

Answer:

Given :-

• The width of the rectangle is 2/3 of its length.
• The perimeter of the rectangle is 80 cm.

To Find :-

• What is the dimensions of the rectangle and also find its area.

Formula Used :-

$\clubsuit$ Perimeter Of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}\: \: \: \bigstar$

$\clubsuit$ Area Of Rectangle Formula :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}\: \: \: \bigstar$

Solution :-

First, we have to find the length and width of the rectangle :

Let,

$\mapsto \bf Length_{(Rectangle)} =\: x\: cm$

Now,

$\bigstar$ The width of the rectangle is 2/3 of its length.

So,

$\implies \sf Breadth_{(Rectangle)} =\: \dfrac{2}{3}\: of\: Length_{(Rectangle)}$

$\implies \sf Breadth_{(Rectangle)} =\: \dfrac{2}{3} \times Length_{(Rectangle)}$

$\implies \sf Breadth_{(Rectangle)} =\: \dfrac{2}{3} \times x$

$\implies \bf Breadth_{(Rectangle)} =\: \dfrac{2x}{3}\: cm$

Now,

$\bigstar$ The perimeter of the rectangle is 80 cm.

Given :

• Length = x cm
• Breadth = $\bf \dfrac{2x}{3}\: cm$

According to the question by using the formula we get,

$\footnotesize \implies \bf Perimeter_{(Rectangle)} =\: 2(Length + Breadth)$

$\implies \sf 80 =\: 2\bigg(x + \dfrac{2x}{3}\bigg)$

$\implies \sf 80 =\: 2\bigg(\dfrac{3x + 2x}{3}\bigg)$

$\implies \sf 80 =\: 2\bigg(\dfrac{5x}{3}\bigg)$

$\implies \sf 80 =\: 2 \times \dfrac{5x}{3}$

$\implies \sf 80 =\: \dfrac{10x}{3}$

By doing cross multiplication we get,

$\implies \sf 10x =\: 3(80)$

$\implies \sf 10x =\: 3 \times 80$

$\implies \sf 10x =\: 240$

$\implies \sf x =\: \dfrac{24\cancel{0}}{1\cancel{0}}$

$\implies \sf x =\: \dfrac{24}{1}$

$\implies \sf\bold{\blue{x =\: 24}}$

Hence, the length and breadth of a rectangle are :

❒ Length of a Rectangle :

$\dashrightarrow \sf Length_{(Rectangle)} =\: x\: cm$

$\dashrightarrow \sf\bold{\purple{Length_{(Rectangle)} =\: 24\: cm}}$

❒ Breadth of a Rectangle :

$\dashrightarrow \sf Breadth_{(Rectangle)} =\: \dfrac{2x}{3}\: cm$

$\dashrightarrow \sf Breadth_{(Rectangle)} =\: \dfrac{2 \times 24}{3}\: cm$

$\dashrightarrow \sf Breadth_{(Rectangle)} =\: \dfrac{48}{3}\: cm$

$\dashrightarrow \sf\bold{\purple{Breadth_{(Rectangle)} =\: 16\: cm}}$

Now, we have to find the area of a rectangle :

Given :

• Length = 24 cm
• Breadth = 16 cm

According to the question by using the formula we get,

$\small \longrightarrow \bf Area_{(Rectangle)} =\: Length \times Breadth$

$\longrightarrow \sf Area_{(Rectangle)} =\: 24\: cm \times 16\: cm$

$\longrightarrow \sf\bold{\red{Area_{(Rectangle)} =\: 384\: cm^2}}$

$\therefore$ The length and breadth of a rectangle is 24 cm and 17 cm respectively and the area of a rectangle is 384 cm² .