Question 488286: Need help please.
The area of a rectangular swimming pool is given by 3x^2+11x+6 ft^2. One side length of the pool is given by 3x + 2 feet. What is an algebraic expression for the other side length of the pool? Simplify this, and include correct units as part of your answer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! area of rectangular swimming pool is equal to 3x^2 + 11x + 6 square feet.
one side of the pool is equal to 3x + 2 feet.
the formula for the area of a rectangle is L * W = A
L is the length
W is the width.
A is the area.
you have A = 3x^2 + 11x + 6
you have L = 3x + 2
if A equals L * W, then:
W = A / L
this would be:
(3x^2 + 11x + 6) / (3x + 2)
we can do the division, or we can determine that this is a quadratic equation whose factors will be (3x + 2) * (x + something).
since 6 is equal to 2 * 3, that something is probably 3.
let's try the factors of (3x + 2) * (x + 3)
we multiply those factors together to get:
3x^2 + 9x + 2x + 6
combine like terms to get 3x^2 + 11x + 6
since this is the quadratic equation that represents the area of the pool, then we have found the width of the pool.
A = L * W = (3x+2) * (x+3)
L = 3x + 2 feet
W = x + 3 feet
we were given the length of the pool as 3x + 2 feet.
the other side of the pool is the width of the pool which is equal to x + 3 feet
if you multiply L * W you will get the area of the pool which is equal to 3x^2 + 11x + 6 square feet
|
|
|
