Question

A farmer wishes to built a fence around a rectangular field; the field is 100 long and 60 ft. wide.The fence will be stone in one side and of wire in three sides, Stone cost Rs 50 per foot and wire cost Rs 20 per foot.How much will be fence cost?​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{In the attachment below there is a rectangular field }ABCD$

       $AB = CD=\text{100 ft}$

       $BC = AD=\text{60 ft}$

       $\text{The farmer is putting stones on side }AD\text{ of the field}$

$\implies \text{Length of the stoned side} = \text{60 ft}$

       $\text{The farmer is putting a fence on the other sides of the field}$

$\implies \text{Length of the fence} = \text{Perimeter of }ABCD - AD$

       $\text{Perimeter of }ABCD = \text{Perimeter of rectangle} = 2(l+b)$

$\implies \text{Perimeter of }ABCD = 2(100+60)$

$\implies \text{Perimeter of }ABCD = 2(160)$

$\implies \text{Perimeter of }ABCD = 320\text{ ft}$

$\implies \text{Length of the fence} = 320 - 60 = 260 \text{ ft}$

       $\text{Rate of stone} = \text{Rs. }50/\text{ft}$

$\implies \text{Cost of putting stones} = AD(\text{Rate of stone})$

$\implies \boxed{\text{Cost of putting stones} = 50 \times 60 = \text{Rs. }1100}$

       $\text{Rate of fence} = \text{Rs. }20/\text{ft}$

$\implies \text{Cost of putting fence} = (\text{Length of fence})(\text{Rate of fence})$

$\implies \boxed{\text{Cost of putting stones} = 260 \times 20 = \text{Rs. }5200}$