Maths-
General
Easy
Question
A fence is put around a rectangular plot of land. The perimeter of the fence is 28 feet. Two of the opposite sides of the fence cost $10 per foot. The other two sides cost $12 per foot. If the total cost of the fence is $148, what are the dimensions of the fence?
Hint:
let the length of plot be l and let the breadth of plot be b
Given total perimeter of the plot = 2(l + b) = 28
Given total cost of fence = cost of fencing length 1 + cost of fencing breadth b
= $148.
The correct answer is: 1 = 10
Ans :- 10 by 4 is the dimensions of the rectangular plot fence
Explanation :-
Step 1:- frame the system of linear equations from given conditions
let the length of plot be 1 and let the breadth of plot be b
Given total perimeter of the plot = 2(1 + b) = 28 
— eq1
let the breadth b fence cost $12 per foot .
let the length 1 fence cost $10 per foot
Given total cost of fence = cost of fencing length 1 + cost of fencing breadth b
cost of fencing length 1 = 1 
cost of fencing per foot .
cost of fencing length 1 = $10(1)
cost of fencing breadth b = b cost of fencing per foot
cost of fencing breadth b = $12(b)
Total cost of fencing be = 10(1) + 12b
10l + 12b = 148 
5l + 6b = 74 — eq 2
Step 2 :- eliminate x to find value of y
Doing 5eq1 - eq2 to eliminate x
We get 5l + 5b = (5l + 6b) = 5(14) = 74
5l + 5b - 5l - 6b = 70 - 74
-b = -4
∴ b = 4
Step 3:- substitute the value of y in eq1 to get the value of x
∴ l = 10.
∴ we get the dimensions of rectangular plot = 10 by 4 (in foots)
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