Question

the length and breadth of a rectangular field are in the ratio 12:7 the boundary has to be fenced which costs ₹275 per metre if the total cost is ₹94050 find the dimensions of the field​

Answer 1

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

The Length of the Rectangle is 108 units and Breadth is 63 units.

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

Given :

Ratio of Length to Breadth = 12 : 7

Rate of Fencing the Rectangle = Rs. 275 per metre

Cost of Fencing = Rs. 94,050

To Find :

The Dimensions of the Rectangle

Solution :

It is given that the total cost of Fencing is Rs. 94,050. The Perimeter of the Rectangle will be the Number which is the quotient when total cost of Fencing is diveded by the rate of Fencing.

$\longrightarrow$ 94050 ÷ 275

$\longrightarrow$ 342

The Perimeter of the Rectangle is 342 units.

◆ $\textbf{\small{\underline{Consider the -}}}$

• Length as 12x
• Breadth as 7x

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

$\longrightarrow$ 2(12x + 7x) = 342

$\longrightarrow$ 24x + 14x = 342

$\longrightarrow$ 38x = 342

$\longrightarrow$ x = 342/38

$\longrightarrow$ x = 9

$\rule{300}{1.5}$

★ Value of 12x

$\longrightarrow$ 12 × 9

$\longrightarrow$ 108

Length = 108 units

$\rule{300}{1.5}$

★ Value of 7x

$\longrightarrow$ 7 × 9

$\longrightarrow$ 63

Breadth = 63 units

$\therefore$ The Length of the Rectangle is 108 units and Breadth is 63 units.

Answer 2

Let the Length be 12x and Breadth be 7x

the Perimeter -

==> 94050 ÷ 275

==> 342

Perimeter ;

2(12x + 7x) = 342

==> 2(19x) = 342

==> 38x = 342

==> x = 342/38

==> x = 9

Length = 12 × 9 = 108

Breadth = 7 × 9 = 63

.°. The Length and Breadth is 108 units and 63 units respectively.