SOLUTION: 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

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
RELATED QUESTIONS
A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the lenght and (answered by checkley71)

A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the lenght and (answered by Nate)

A landscape designer is designing a garden with three features: a sundial, a birdbath,... (answered by stanbon)

A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and (answered by nerdybill)

A farmer has a rectangular garden plot surrounded by 220 feet of fence. Find the... (answered by checkley77)

A farmer has a rectangular garden plot surrounded by 120ft of fence. Find the length and... (answered by josmiceli)

A rectangular garden plot is surrounded by 20 meters of fence. Find the length and the... (answered by josgarithmetic)

the total height of a 1-foot tall birdbath if its placed on a base that is b feet tall? (answered by RAY100)

Gloria had a rectangular garden plot last year with an area of 60 square feet. This year... (answered by ankor@dixie-net.com)