SOLUTION: A large rectangular movie screen in an IMAX theater has an area of 10,591 square feet. Find the dimensions of the screen if it is 30 feet longer than it is wide.
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Question 1174204: A large rectangular movie screen in an IMAX theater has an area of 10,591 square feet. Find the dimensions of the screen if it is 30 feet longer than it is wide. Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52775) (Show Source):
Let W be the width, in feet.
Then the length is (W+30) feet, and the area equation is
W*(W+30) = 10591 square feet.
Solve this quadratic equation to find W (accept a positive root, only).
Then calculate the length W+30.
You can try to factor this, by finding two numbers whose product is 10591 and whose difference is 30. But that is what the original problem asks you to do -- so the use of formal algebra doesn't get you any closer to the solution.
Alternatively, you can always solve a quadratic equation using the quadratic formula. But with this equation, the calculations are ugly.
By far the easiest way to solve the problem is to find the prime factorization of 10591 and use it to find the solution.
There are many prime factorization calculators on the internet; they will show you
10591 = 7*17*89
It takes only a moment to combine the first two prime factors to find the solution to the problem:
10591 = 119*89
ANSWER: the dimensions of the rectangular screen are 89 by 119 feet.
