SOLUTION: The length of a rectangle is 5 m less than three times the width. a. If the width of the rectangle is x, write an expression for the length of the rectangle terms of x. b.

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Question 1119313: The length of a rectangle is 5 m less than three times the width.
a. If the width of the rectangle is x, write an expression for the length of the rectangle terms of x.
b. Based on the above situation write an expression for the area of a rectangle in terms of x. (A=l*w)
c. If the area of the rectangle is 28 m^2. Find the dimensions of the rectangle.
(use the information from part b)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the width. Three times the width is . 5 less than 3 times the width is then , which is the length.



But if , then



Solve the quadratic for . Since we know by inspection (the sign on the constant term is the opposite of the sign on the lead coefficient) that there are two real number roots for this equation, and because the sign on the constant term is negative we know that these two roots must have opposite signs, we know that one of the roots will be less than zero. Hence, only one of the roots of this equation will be valid because a negative value for length defies the laws of physics. The width will be the positive root. Then calculate to find the length.


John

My calculator said it, I believe it, that settles it