SOLUTION: The perimeter of a garden is 66 meters and its area is 270 m2. Find the dimensions of the garden.

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Question 916118: The perimeter of a garden is 66 meters and its area is 270 m2. Find the dimensions of the garden.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions x and y;
p=66
xy=270
Use A=xy

The question happens often as an academic exercise.
A, p known.
x, y unknown.

2x+2y=p and xy=A.
2y=p-2x
y=%28p-2x%29%2F2
-
x%28p-2x%29%2F2=A
x%28p-2x%29=2A
xp-2x%5E2=2A
-2x%5E2%2Bxp-2A=0
2x%5E2-xp%2B2A=0

You can continue symbolically like this and use formula for solution of a quadratic equation, or you can substitute the given values for p and A now, and reach your values for x and y.

2x%5E2-66x%2B2%2A270=0
x%5E2-33x%2B270=0

x=%2833%2B-+sqrt%2833%5E2-4%2A270%29%29%2F2
x=%2833%2B-+sqrt%289%29%29%2F2
x=%2833%2B-+3%29%2F2

The dimensions are 15 and 18.