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A large rectangular movie screen in an Imax theater has an area of 6,984 square feet. Find the dimensions of the screen if it is 25 feet longer than it is wide. i need length and width

Verified Answer :

greyhoundbloke

The area of a rectangle is length L times width W.
Area = L W.
We are told that L = W + 25.
So if the area = L W
We can substitute L with W + 25 to give us
6984 = L W = (W + 25 ) W = W^2 + 25W.
W^2 + 25W = 6984. We can turn this into a quadratic equation by removing 6984 from both sides
W^2 + 25W - 6984 = 0
To solve a quadratic  ax^x + bx + c = 0 we use this formula
\((-b+/- \sqrt{-b^{2} -4ac})/2a\)
In our quadratic a = 1, b=25, c=-6984
-b = -25
b2 - 4ac = 2525 - 4 1 -6984 = 625 + 27936 = 28561
SQRT(28561) = 169
So we have two answers (from the +/- in the quadratic solver)
(-b+169)/(21) = (-25+169)/2 = 144/2 = 72or(-b-169)/(21) = (-194)/2 = -97Since we can't have a negative length, 72 must be the value for W
If W is 72 then L = W + 25 = 97 
We can now test this by saying A = L W = 97 * 72 = 6984, the original area given.

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