SOLUTION: An engineer is designing a rectangular computer screen to have an area of 150 square inches and a diagonal of 18 inches. Which of the following equations could the engineer s

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Question 283963: An engineer is designing a rectangular computer screen to have an
area of 150 square inches and a diagonal of 18 inches. Which of the
following equations could the engineer solve to find the value of x,
the length of a side of the screen?
A. x2 – 18x + 150 = 0

B. x2 – 324x + 22,500 = 0

C. x4 – 324x2 + 22,500 = 0

D. x4 + 324x2 – 22,500 = 0



Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!



The diagonal, which is 18 inches is the hypotenuse of
the right triangle with legs x and y. Using the
Pythagorean theorem, we have the equation:

x%5E2%2By%5E2=18%5E2
x%5E2%2By%5E2=324 

The area of the whole rectangle given as 150 square inches 
is the length x times the width y.  So we have the 
equation:

xy=150

So we have the system:

system%28x%5E2%2By%5E2=324%2Cxy=150%29

Solve the second equation for y

xy=150
y=150%2Fx

Now we substitute 150%2Fx for y in the
equation:

x%5E2%2By%5E2=324
x%5E2%2B%28150%2Fx%29%5E2=324
x%5E2%2B150%5E2%2Fx%5E2=324
x%5E2%2B22500%2Fx%5E2=324

Multiply through by x%5E2 to clear of fractions:

x%5E4%2B22500=324x%5E2

Get 0 on the right by subtracting 324x%5E2 from
both sides:

x%5E4%2B22500-324x%5E2=0

Get it in descending order:

x%5E4-324x%5E2%2B22500=0

That is choice (C).

Edwin