SOLUTION: A large rectangular movie screen in an IMAX theater has an area of 10,509 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide.

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Question 1122019: A large rectangular movie screen in an IMAX theater has an area of 10,509 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide.
Found 4 solutions by josgarithmetic, greenestamps, ikleyn, Alan3354:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Dimensions are x and x+20, width and length.




If you look at prime factorization you might avoid trying to solve as a quadratic equation.

, differing by 20

---------the dimensions
Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


If you try to use algebra to form an quadratic equation for the problem, you will end up having to try to find two numbers whose difference is 20 and whose product is 10509. But that's what the original problem asks you to do -- so formal algebra doesn't help any.

As the other tutor suggested, you might want to try to use the prime factorization of 10509 to find the answer.

However, finding the prime factorization of 10509 is not an easy task, because most of the prime factors are relatively large.

So use logical analysis instead.

(1) The two numbers differ by 20, so they have the same units digit.
(2) You want the product of the two numbers to be 10509. To get a units digit of 9 in the product of the two numbers, the units digit of the two numbers has to be either 3 or 7.
(3) The desired product 10509 is a bit more than 10000, which is 100*100. So the two most likely candidates for the two numbers are 93 and 113, or 97 and 117.

Trying those two pairs finds that the two numbers are 93 and 113.

So the screen is 93x113 feet.
Answer by ikleyn(52878)   (Show Source): You can put this solution on YOUR website!
.

Let me show you a quick, elegant and unexpected method of solving such problems. 


Let x be the number (now unknown) which is exactly half way between the width and the length of the playground.


Then, as you understand,  the length = (x+10) inches and  the width = (x-10) inches.


The area = 10509 = length*width = (x+10)*(x-10).


Thus (x+10)*(x-10) = 10509,  which implies   = 10509,  i.e.   = 10509+100 = 10609.


Hence, x =  = 103.


Then the length = 103+10 = 113  and the width = 103-10 = 93.

Answer. The dimensions of the screen are 113 inches and 93 inches.

Solved.

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See the lesson
    - Three methods to find the dimensions of a rectangle when its area and the difference of two dimensions are given
in this site.


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A large rectangular movie screen in an IMAX theater has an area of 10,509 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide.
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Yet another method:
Make use of the quadratic equation to factor big numbers:
----
x*(x+20) = 10509

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=42436 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 93, -113. Here's your graph:

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