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Please check the attached file for the diagram of Sally's yard.
Let be the width of the yard.
Let be the length.
We are given that the length of the yard is 8 feet more than 4 times the width. Let us convert this into a mathematical equation.
4 times the width will be . Now, 8 feet, or 8 more than 4 times the width will be
. We know that this is the value of the length of the yard and thus we can write this as:
As we can see we have found the relationship between the length, and the width,
of the yard.
We have been told that the total length of the fence required for the yard is 106 feet. This obviously means that the perimeter of the rectangular yard is 106 feet.
Now, we know that the perimeter of a rectangle is given by:
Perimeter= this is because we know that the length,
is given by
.
Continuing further we get:
This is because Perimeter=length of the fence=106 (given)
Therefore,
or, so, we just now found the width of the yard which is 9 feet. We are required to find the length. We can easily find the length using the relationship between
and
which is:
giving us:
Thus the length of the fence is 44 feet.
