Question

The length and breadth of a rectangular field are in the ratio $4:3$. Its area is $6,912m^2$. Find the cost of fencing at Rs. $2.50$ per metre.

• A. $240$ Rs.
• B. $420$ Rs.
• C. $840$ Rs.
• D. $1240$ Rs.

Answer 1

The correct option is C $840$ Rs.

Given:

The ratio of length and breadth of the rectangular field is

$l:b=4:3$

$\Rightarrow \frac{l}{b}=\frac{4}{3}$

$\Rightarrow l=\frac{4}{3}b.........\left(1\right)$

The area of the rectangular field is

$l\times b=6912m^2........\left(2\right)$

put value of $l$ from equation (1) to equation (2)

$\frac{4b}{3}\times b=6912m^2$

$\Rightarrow b^2=6912\times \frac{3}{4}{m}^2$

$\Rightarrow b^2=5184m^2$

$\Rightarrow b=\sqrt{5184}m$

$\Rightarrow b=72m.......\left(3\right)$

Put value of $b$ from equation $\left(3\right)$ in equation $\left(1\right),$ we get

$l=\frac{4}{3}\times 72m$

$\Rightarrow l=96m.......\left(4\right)$

The parameter of the rectangular field is

$2(l+b)=2\times (96+72)m$

$=2\times 168m$

$=336m$

Given,

Cost of fencing $1m=2.50Rs.$

Hence, Cost of fencing $336m=2.50\times 336Rs.=840Rs.$

Thus, Cost of fencing the rectangular field is $840Rs.$