SOLUTION: Find the length x if the shaded area is 480 cm^2. The shape is a trapezoid. What I've got so far is this: 480 = x^2 + 2x x^2 + 2x + 48 = 0 Am I on the right track? If

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find the length x if the shaded area is 480 cm^2. The shape is a trapezoid. What I've got so far is this: 480 = x^2 + 2x x^2 + 2x + 48 = 0 Am I on the right track? If       Log On


   

Question 120875This question is from textbook College Algebra
: Find the length x if the shaded area is 480 cm^2.
The shape is a trapezoid.
What I've got so far is this:
480 = x^2 + 2x
x^2 + 2x + 48 = 0
Am I on the right track? If so, what do I do next? Thank you for your help!! This question is from textbook College Algebra

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Very difficult to tell whether you have the first step correct or not, because you didn't specify which part of the trapezoid was labeled x. Since the area of a trapezoid is given by A=%28%28a%2Bb%29h%29%2F2 and you started with 480+=+x%5E2+%2B+2x, I'm going to assume that the height is x, and the two bases are 2x and 4 respectively.

A=%28%282x%2B4%29x%29%2F2
A=%28x%5E2%2B2x%29, and since the area is 480,

x%5E2%2B2x=480

Assuming that is correct, on to the next step. Here you have an error.

x%5E2%2B2x=480

Add -480 to both sides:

x%5E2%2B2x-480=0

This does not factor nicely. Use the quadratic formula.

x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-480%29%29%29%2F%282%29+
x+=+%28-2+%2B-+sqrt%28+1924%29%29%2F2
x+=+%28-2+%2B-+2%2Asqrt%28481%29%29%2F2

This ugliness leads me to believe that the initial setup is not correct. Describe the figure in more detail.