Question

the side of a rectangle are in the ratio 2 ratio 3.find its side if it's perimeter is 20 ​

Answer 1

$\bf\huge\underline{Answer}$

The sides of the rectangle are 4 cm and 6 cm respectively.

Explanation :-

Given :

• Ratio of the sides of rectangle - 2 : 3
• Perimeter of the rectangle - 20 cm

To find :

The sides of the rectangle

Solution :

Let the first side of the rectangle be 2x

And the second side of the rectangle be 3x

We know that,

Perimeter = 2 (Length + Breadth)

=> Perimeter = 20 cm

=> 2(2x + 3x) = 20

=> 2 × 5x = 20

=> 10x = 20

=> x = 20/10

=> x = 2

Hence, the value of x is 2

Now,

The first side => 2x = 2 × 2 = 4 cm

The second side => 3x = 3 × 2 = 6 cm

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Length of the Rectangle is 6 units and Breadth is 4 units.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Ratio of the Length and Breadth of the Rectangle = 2 : 3

Perimeter of the Rectangle = 20

To Find :

The Dimensions of the Rectangle

Solution :

Consider the -

• Breadth as 2x
• Length as 3x

★ Perimeter = $\boxed{\sf{2(Length+Breadth)}}$

$\sf{\longrightarrow} \: 2(3x + 2x) = 20$

$\sf{\longrightarrow} \: 6x + 4x = 20$

$\sf{\longrightarrow} \: 10x = 20$

$\sf{\longrightarrow} \: x = \dfrac{20}{10}$

$\sf{\longrightarrow} \: x = 2$

$\rule{300}{1.5}$

★ Value of 2x

$\sf{\longrightarrow} \: 2 \times 2$

$\sf{\longrightarrow} \: 4$

Breadth is 4 units

$\rule{300}{1.5}$

★ Value of 3x

$\sf{\longrightarrow} \: 3\times 2$

$\sf{\longrightarrow} \: 6$

Length is 6 units.

$\therefore$ The Length of the Rectangle is 6 units and Breadth is 4 units.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\sf{\longrightarrow} \: 2(4 + 6) = 20$

$\sf{\longrightarrow} \: 8 + 12 = 20$

$\sf{\longrightarrow} \: 20 = 20$

$\therefore$ The Length of the Rectangle is 6 units and Breadth is 4 units.