Question

The length and width of a rectangle are in the ratio 3:2 .If the perimeter is 100 cm, what is the area of the rectangle

Answer 1

Answer:

600 cm²

Step-by-step explanation:

We know that:

• $Length:Breadth = 3:2$

Solution:

• $Length:Breadth = 3:2$
• => $Length:Breadth = 3x:2x$
• => $3x + 2x + 3x + 2x=100 cm$
• => $10x=100 cm$
• => $x = 10 cm$
• => $Length = 30 cm$
• => $Breadth = 20cm$
• => $Area_{rectangle} = 30(20) cm^{2}$
• => $Area_{rectangle} = 600 cm^{2}$

Hoped this helped!

Answer 2

First of all We will find the length and breadth with the help of perimeter and then find the area...

Ratio of length to breadth is 3:2, So let length be 3x and breadth be 2x

ATQ,

$\boxed{ \mathfrak{perimeter = 2(l + b)}}$

$\tt \: 100 = 2 \times (3x + 2x)$

$\tt \: 50 = 3x + 2x$

$\tt \: 50 = 5x$

$\tt \: 10 = x \: or \: x = 10$

Now,

$\sf \: length = 3x \\ \sf= 3 \times 10 \\ \sf \: = 30 \: cm$

$\sf \: breadth = 2x \\ \sf= 2 \times 10 \\ \sf \: = 20 \: cm$

Finding area⤵️

$\boxed{ \mathfrak{area = l \times b}}$

$\tt \: area = 30 \times 20 \\ \tt \: = 600 {cm}^{2}$