Question 302458: Here is a problem that requires factoring to solve:
A rectangular garden plot has a birdbath with a square base in its center, The length of the garden is 4 more than twice the length of a side of the base of the birdbath, and the width of the garden is 7 more than the length of the side of the base of the birdbath. If the area of the garden available for planting vegetables is 47 square feet, what are the dimensions of the garden and the dimensions of the base of the birdbath?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular garden plot has a birdbath with a square base in its center,
The length of the garden is 4 more than twice the length of a side of the base of the birdbath,
and the width of the garden is 7 more than the length of the side of the base of the birdbath.
If the area of the garden available for planting vegetables is 47 square feet,
what are the dimensions of the garden and the dimensions of the base of the birdbath?
:
Let x = one side of the square birdbath base
:
"The length of the garden is 4 more than twice the length of a side of the base of the birdbath,"
L = 2x + 4
:
"the width of the garden is 7 more than the length of the side of the base of the birdbath."
W = x + 7
:
what are the dimensions of the garden and the dimensions of the base of the birdbath?
:
Garden area - birdbath base area = 47
(2x+4)(x+7) - x^2 = 47
FOIL
2x^2 + 14x + 4x + 28 - x^2 = 47
:
2x^2 - x^2 + 18x + 28 - 47 = 0
A quadratic equation
x^2 + 18x - 19 = 0
Factors to
(x + 19)(x - 1) = 0
the positive solution
x = 1 ft is the base of the birdbath
then
2(1) + 4 = 6' is the length of the garden
1 + 7 = 8' is the width
:
Check
6 * 8 = 48 sq ft dimension of the garden
subtract 1 sq/ft for the birdbath and you 47 sq/ft of planting area
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