Question

3.
The perimeter of rectangle is 320m, its sides are in the ratio of 5:3 then its area is -
a) 6000 m
b) 3000 m
c) 12000 m
d) 24000 m​

Answer 1

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

Option a)

6000 m²

The area of the Rectangle is 6000 m².

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

Given :

Perimeter of the Rectangle = 320 m

Ratio of the sides = 5 : 3

To Find :

The area of the Rectangle

Solution :

Consider the -

• Length as 5x
• Breadth as 3x

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

$\sf{\longrightarrow} \: 2(5x + 3x) = 320$

$\sf{\longrightarrow} \: 10x + 6x = 320$

$\sf{\longrightarrow} \: 16x = 320$

$\sf{\longrightarrow} \: x = \dfrac{320}{16}$

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

$\rule{300}{1.5}$

★ Value of 5x

$\sf{\longrightarrow} \: 5 \times 20$

$\sf{\longrightarrow} \: 100$

Length = 100 m

$\rule{300}{1.5}$

★ Value of 3x

$\sf{\longrightarrow} \: 3 \times 20$

$\sf{\longrightarrow} \: 60$

Breadth = 60 m

Length of the Rectangle is 100 m and Breadth is 60 m

$\rule{300}{1.5}$

As we got the dimensions of the Rectangle, we can niw find the Area of the Rectangle.

★ Area = $\boxed{\sf{Length \times Breadth}}$

$\sf{\longrightarrow} \: 100 \times 60$

$\sf{\longrightarrow} \: 6000$

$\therefore$ The area of the Rectangle is 6000 m².

Answer 2

According to the given question:-

320m is the Perimeter of the Rectangle

5:3 is the Ratio of Sides

Here we need to find the area of the rectangle:-

Let 5x be the length

Let 3x be the breadth

Formula:-

$Perimeter = 2(l + b)$

$= > 2(5x + 3x) = 320$

$= > 10x + 6x = 320$

$= > 16x = 320$

$= > x = \frac{320}{16}$

$= > x = 20$

Here the value of 5x is

$= > 5 \times 20$

$= > 100$

Here the value of 3x is

$= > 3 \times 20$

$= > 60$

So, the breadth of 60m

Area = L × B(Length × Breadth)

$= > 100 \times 60$

$= > 6000$

Therefore, the 6000 is the answer:-