A large rectangular movie screen in an IMAX theater has an area of 7,326 square feet. Find the dimensions of the screen if it is 25 feet longer than it is wide.

Answer 1

As large as this looks it can be factored, first you might want to test the digits in 7326 it is divisible by multiples of 9, this number is just over 7300 (100 x 73) you should consider factors of it as being at least two digits each, and finally while it is divisible by 9 it is an even number so one factor will be some 2 digit multiple of 9 and another will be an even number. The difference between the two factors of 7326 must be 25 most likely the odd multiple of 9 minus the even number.

Factors of 7326 include 3, 9, 11, 33, 37, and 2. (11 x 9) - (37 x 2) = 25

and (3 x 33) - (37 x 2)= 99 - 74 = 25

You could also just try the factors in a Quadratic Equation using the area.

Since Area = L x W

L = W + 25

we have an Area 7326 = W(W + 25)

7326 ft² = W² + 25W

0 = W² + 25W - 7326

(W + 99)(W - 74)

W=74 only since it cannot be -99

but we know the W +25 = L

So L = 74 + 25 = 99 (the two digit multiple of 9)

By the way 99 x 74 = 7326

The screen is 99 ft long by 74 ft wide

Answer 2

X(X+25) = 7326

x^2 + 25x = 7326

x^2 + 25x - 7326 = 0

Factoring via AC method:

7326 = 2 * 3663 = 2 * 3 * 1221 = 2 * 3 * 3 * 407 = 2 * 3 * 3 * 11 * 37

99 - 74 = 25 ---> 3*3*11 - 2*37 = 25

x^2 + 99x - 74x - 7326 = 0

x(x+99) - 74( x + 990 = 0

(x+99)(x-74) = 0

x+99=0 results in negative measures

x=74.

the width is 74, the length is 99