SOLUTION: A rectangular pond's length is twice its width. The pond is surrounded on all sides by a three foot wide garden. A) write a function, A(x), for the area of the pond including the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rectangular pond's length is twice its width. The pond is surrounded on all sides by a three foot wide garden. A) write a function, A(x), for the area of the pond including the      Log On


   

Question 515173: A rectangular pond's length is twice its width. The pond is surrounded on all sides by a three foot wide garden.
A) write a function, A(x), for the area of the pond including the sidewalk,IN TERMS OF THE WIDTH OF THE POND.
B) if the total area (including the garden)is 99 square feet, what are the dimensions of the pond?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
width =x
length =2x
side walk = 3 ft
width including sidewalk = x+6
length including sidewalk = 2x+6
Area = L*W
Area = (x+6)(2x+6)
A(x) = 2x^2+18x+36
----
2x^2+18x+36 =99
2x^2+18x+36-99=0
2x^2+18x-63=0
Find the roots of the equation by quadratic formula

a= 2 ,b= 18 ,c= -63

b^2-4ac= 324 + 504
b^2-4ac= 828
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2B21%29%2F%284%29
x1=( -18 + 28.77 )/ 4
x1= 2.69
x2=( -18 -28.77 ) / 4
x2= -11.69
Ignore negative value
Dimensions of pool
width = 2.69 ft
length = 5.38 ft
m.ananth@hotmail.ca