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The total cost of fencing a rectangular field at rupees 40 per metre is rupees 8400 if the length of the field is 60 find the perimeter of the rectangle and breadth of the rectangle
Given: The total cost of fencing a rectangular field at rupees $40$ per metre is rupees $8400$
the length of the field is $60$
To Find: The perimeter of the rectangle and breadth of the rectangle
Solution
Cost of fencing per meter = 40₹
The total cost of fencing the rectangle = 8400₹
a ) Fencing should be done on the boundary of the field, so it is related to the perimeter.
Perimeter = $\frac{Total cost of fencing the rectangle}{Cost of fencing per meter}$
= $\frac{8400}{40}$ = 210
Perimeter of Rectangle = $210$ m
b ) Formula of Perimeter = $2 (length + breadth)$
length = $60$ m
$210 = 2 (60 + breadth)$
Rewrite,
$2 (60 + breadth) = 210$
60 + breadth = $\frac{210}{2}$
60 + breadth = 105
breadth = $105 - 60 = 45$
breadth = $45$ m.
Therefore the breadth is $45$ m and the perimeter is $210$m