SOLUTION: A large rectangular movie screen in an Imax theater has an area of 8,364 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide.
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Question 498427: A large rectangular movie screen in an Imax theater has an area of 8,364 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide. Answer by solver91311(24713) (Show Source):
If a rectangle has an area of square units and the length, is units longer than the width, , find the dimensions.
The length can be expressed as and the width as simply . The product of the length times the width is the area, so:
A little algebra music there Maestro!
And we have a quadratic. Since the constant term (the ) is negative, we are assured that the signs on the binomial factors are opposite and therefore the roots have opposite signs. Since we are looking for a positive measure of length we can discard the negative root. The quadratic formula solution to the general problem is therefore:
Just plug in the given difference and the given area and then do the arithmetic.
John
My calculator said it, I believe it, that settles it
