Answer:
The length of the fence needed to surround this garden is 188 meters.
Step-by-step explanation:
Given : A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10 m greater than the other side.
To find : The length of the fence needed to surround this garden if the area of the vegetable garden is 2184 m² ?
Solution :
Let the one side of rectangle be 'x'.
Then the other side is 'x+10'.
The area of the rectangle is 2184 m²,
i.e. [tex]x(x+10)=2184[/tex]
[tex]x^2+10x-2184=0[/tex]
Solve by middle term split,
[tex]x^2+52x-42x-2184=0[/tex]
[tex]x(x+52)-42(x+52)=0[/tex]
[tex](x+52)(x-42)=0[/tex]
[tex]x=-52,42[/tex]
Reject negative value,
The side of the rectangle is 42 m.
The other side is 42+10=52 m
The perimeter of the rectangle is [tex]P=2(l+b)[/tex]
[tex]P=2(42+52)[/tex]
[tex]P=2(94)[/tex]
[tex]P=188[/tex]
Therefore, the length of the fence needed to surround this garden is 188 meter.
