Rita has 88 feet of fencing. She wants to use this fencing to enclose a rectangular area of 480 square feet. What must the dimensions of her rectangular enclosure be?
x*y = 480
2x + 2y = 88
solve for x and y, the width and length
To find the dimensions of the rectangular enclosure, we can set up two equations. Let's say the length of the rectangular enclosure is L and the width is W.
First, let's establish the equation for the perimeter of the enclosure:
2L + 2W = 88
Since she wants to use 88 feet of fencing, the sum of all the sides should add up to 88 feet.
Next, let's establish the equation for the area of the enclosure:
L * W = 480
Since she wants the area of the enclosure to be 480 square feet, the length multiplied by the width should equal 480.
Now we have a system of equations:
2L + 2W = 88
L * W = 480
To solve this system, we can use substitution or elimination method.
Let's solve by substitution:
Rearrange the first equation to solve for L: 2L = 88 - 2W
L = (88 - 2W) / 2
Substitute this value of L in the second equation:
((88 - 2W) / 2) * W = 480
Simplify the equation:
(88 - 2W) * W = 960
Distribute the W:
88W - 2W^2 = 960
Rearrange to a quadratic equation form:
2W^2 - 88W + 960 = 0
Factor the quadratic equation:
(W - 40)(2W - 24) = 0
Set each factor equal to zero and solve for W:
W - 40 = 0 or 2W - 24 = 0
If W = 40, substituting into the area equation:
L * 40 = 480
L = 480 / 40 = 12
If W = 12, substituting into the area equation:
12 * L = 480
L = 480 / 12 = 40
So, the dimensions of her rectangular enclosure must be 40 feet by 12 feet.