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mihalych1998 [28]
3 years ago
15

Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the s

ame amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet. What is the quadratic equation that would model this scenario?
Mathematics
2 answers:
Naddika [18.5K]3 years ago
7 0
For the square, the area will be 4x4, which will equal 16 sq ft. Since Juan is wanting to turn it to a rectangle, he will have to use the equation 8x2.
alukav5142 [94]3 years ago
7 0
Here is the model, but the Areas are not the same.
Old = X*X = X^2 Area
New = 2X*(X-16) = 2X^2-32X
If the Areas are the same,
2X^2 - 32X = X^2
X^2 - 32X = 0
X(X-32) = 0
X = 32
Old Area = 32x32 = 1024 ft^2
New Area = 2(32x32) = 32x32 = 1024 ft^2
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The angle, from E to N, can be calculated as:

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If we want to express it from N to E, we substract the angle from 90°:

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