Question

A wire is 72 cm long. It is bent to form a rectangle. The ratio of its length to its breadth is 7:5 Find the area of the rectangle.​

Answer 1

Answer:

Given :-

• A wire is 72 cm long.
• It is bent to form a rectangle.
• The ratio of its length to its breadth is 7 : 5.

To Find :-

• What is the area of the rectangle.

Solution :-

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

Let,

$\mapsto \bf Length_{(Rectangle)} =\: 7x\: cm$

$\mapsto \bf Breadth_{(Rectangle)} =\: 5x\: cm$

Given :

• Perimeter = 72 cm

As we know that,

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

According to the question by using the formula we get,

$\implies \sf 2(7x + 5x) =\: 72$

$\implies \sf 7x + 5x =\: \dfrac{\cancel{72}}{\cancel{2}}$

$\implies \sf 12x =\: 36$

$\implies \sf x =\: \dfrac{\cancel{36}}{\cancel{12}}$

$\implies \sf\bold{\blue{x =\: 3}}$

Hence, the required length and breadth is :

$\footnotesize \dashrightarrow \sf\bold{\purple{Length_{(Rectangle)} =\: 7x =\: 7 \times 3 =\: 21\: cm}}$

$\footnotesize \dashrightarrow \sf\bold{\purple{Breadth_{(Rectangle)} =\: 5x =\: 5 \times 3 =\: 15\: cm}}$

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

As we know that :

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

Given :

• Length = 21 cm
• Breadth = 15 cm

According to the question by using the formula we get,

$\implies \sf Area_{(Rectangle)} =\: 21\: cm \times 15\: cm$

$\implies \sf\bold{\red{Area_{(Rectangle)} =\: 315\: cm^2}}$

$\therefore$ The area of the rectangle is 315 cm² .

Answer 2

It is given that 72 cm long wire is bent to form a rectangle

Also, the ratio of the length and breadth of the rectangle is 7:5

The length of the wire will be the perimeter of the rectangle

We will first the length and breadth of the rectangle

Let the length and breadth be 7x and 5x respectively

So, perimeter = 2 ( length + breadth)

72 = 2 ( 7x + 5x)

36 =12x

x = 3

so, length = 7x

= 7 × 3

= 21

breadth = 5x

= 5 × 3

= 15

So , area = length × breadth

= 21 × 15

= 315 cm²

Hence, the area will be 315 cm²