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?
:
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