Given
Shape of garden: Rectangle
Perimeter: 34 meters
Area: 72 square meters
Length of one side = x
Required
Find the dimension of the rectangle
Let the length of the other side of the rectangle be represented with y.
We start by writing out the perimeter of a rectangle
Perimeter, P = 2(L + B)
Where P is the perimeter; L and B are the length and width of the sides of the rectangle.
In this case L and B are represented by x and y
So,
P = 2(x + y)
By substituting 34 for P
34 = 2(x + y)
Multiply both sides by ½
½ * 34 = ½ * 2(x + y)
17 = x + y
Make y the subject of formula
y = 17 - x
Recall that the sides of the rectangle are represented by x and y.
Hence, the area of the rectangle is as follows.
Area = x * y
Substitute 72 for Area and 17 - x for y
72 = x(17 - x) --- Open bracket
72 = 17x - x² ---- Reorder
x² - 17x + 72 = 0
Now, we have a quadratic equation
Solving by factorisation
x² - 8x - 9x + 72 = 0
x(x - 8) - 9(x - 8) = 0
(x - 8)(x - 9) = 0
x - 8 = 0 or x - 9 = 0
x = 8 or x = 9
Recall that
y = 17 - x.
When x = 8
y = 17 - 8
y = 9
When x = 9
y = 17 - 9
y = 8
Writing out the result, we have
x = 8 , y = 9
Or
x = 9, y = 8
Hence, the dimension of the rectangle is 8 metres by 9 metres
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