Question

The length and breadth of a rectangular piece of land r in the ratio 5:3.If the total cost of fencing at rupees 7 per metre is rupees 2800.Find the area of the plot

Answer 1

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

The area of the Rectangle is 9375 sq. unit.

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

Given :

Length and Breadth of the Rectangle = 5 : 3

Rate of Fencing = Rs. 7 per m.

Cost of Fencing = Rs. 2800

To Find :

The area of the Rectangle

Solution :

First find the Perimeter of the Rectangle

Divide 2800 by 7

$\sf{\implies} \: 2800 \div 7$

$\sf{\implies} \: 400$

Perimeter = 400

$\rule{300}{1.5}$

Consider the :

• Length as 5x
• Breadth as 3x

★ $\boxed{\sf{2(Length+Breadth)}}$

$\sf{\implies} \: 2(5x + 3x) = 400$

$\sf{\implies} \:10x + 6x = 400$

$\sf{\implies} \:16x = 400$

$\sf{\implies} \:x = \dfrac{400}{16}$

$\sf{\implies} \:x = 25$

$\rule{300}{1.5}$

★ Value of 5x

$\sf{\implies} \:5 \times 25$

$\sf{\implies} \:125$

★ Value of 3x

$\sf{\implies} \:3 \times 25$

$\sf{\implies} \:75$

Length = 125 unit

Breadth = 75 unit

$\rule{300}{1.5}$

Find Area of the Rectangle

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

$\sf{\implies} \: 125 \times 75$

$\sf{\implies} \: 9375$

$\therefore$ The area of the Rectangle is 9375 sq. unit.

Answer 2

Answer:-

• 5 : 3 is length and breadth of Rectangle
• ₹ 7 per/m Rate of Fencing
• Rs. 2800 is the Cost of Fencing

2800÷7

400 is the perimeter

5x is the length

3x is the breadth

$=2(5x+3x)=400$

$=10x+6x=400$

$=16x=400$

$=x= 16400$

$=x=25$

(Eq) 1

$=5×25$

$=125$

(Eq) 2

$=3×25$

$=75$

• 125 unit is the length
• 75 unit is the breadth

(Area=L×B)

$=125×75$

$=9375$

Therefore, 9375 is the area of plot

$:)$