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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?

hintHint:

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 not stretchy rightwards double arrow l plus b equals 14  — 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 cross times cost of fencing per foot .
    cost of  fencing length 1   = $10(1)
    cost of  fencing breadth b =cross times b cross timescost of fencing per foot
    cost of  fencing breadth b  = $12(b)
    Total cost of fencing be  = 10(1) + 12b
    10l + 12b = 148 rightwards double arrow5l + 6b = 74 — eq 2
    Step 2 :- eliminate x to find value of y
    Doing  5cross timeseq1 - eq2 to eliminate x
    We get 5l + 5b = (5l + 6b) = 5(14) = 74
    rightwards double arrow5l + 5b - 5l - 6b = 70 - 74
    rightwards double arrow -b = -4
    ∴ b = 4
    Step 3:- substitute the value of y in eq1 to get the value of x
    l plus b equals 14 not stretchy rightwards double arrow l plus 4 equals 14
    not stretchy rightwards double arrow l equals 14 minus 4
    ∴ l = 10.
    ∴ we get the dimensions of rectangular plot = 10 by 4 (in foots)

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