Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.


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

Sagot :

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
[tex](-b+/- \sqrt{-b^{2} -4ac})/2a [/tex]
In our quadratic a = 1, b=25, c=-6984
-b = -25
b2 - 4ac = 25*25 - 4 * 1 * -6984 = 625 + 27936 = 28561
SQRT(28561) = 169
So we have two answers (from the +/- in the quadratic solver)
(-b+169)/(2*1) = (-25+169)/2 = 144/2 = 72or(-b-169)/(2*1) = (-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.

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.