SOLUTION: Megan's backyard has a small pound that is 15 feet by 10 feet. her mother wants to add a wooden deck pathway around the pound, so that the area of the pool and deck is 234 ft squa

Question 632410: Megan's backyard has a small pound that is 15 feet by 10 feet. her mother wants to add a wooden deck pathway around the pound, so that the area of the pool and deck is 234 ft squared. how wide does the pathway need to be to fulfill Megan's mom's request?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Megan's backyard has a small pound that is 15 feet by 10 feet.
her mother wants to add a wooden deck pathway around the pound, so that the
area of the pool and deck is 234 ft squared.
how wide does the pathway need to be to fulfill Megan's mom's request?
:
Let x = the width of the pathway around the pond
then the over all dimensions: (2x+15) by (2x+10)
The Area
(2x+15)*(2x+10) = 234
FOIL
4x^2 + 20x + 30x + 150 = 234
4x^2 + 50x + 150 - 234 = 0
4x^2 + 50x - 84 = 0
Simplify, divide by 2
2x^2 + 25x - 42 = 0
You can use the quadratic formula, but this will factor to:
(2x-3)(x+14) = 0
the positive solution
2x = 3
x = 1.5 ft is the width of the walkway
:
:
Check this by finding the area with this value
(2(1.5)+15) * (2(1.5)+10) = 234
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