SOLUTION: The length of a rectangular parking lot is 36m longer than its width. The area of the parking lot is 5,152m2. If the area of the parking lot is double, would its length and width a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The length of a rectangular parking lot is 36m longer than its width. The area of the parking lot is 5,152m2. If the area of the parking lot is double, would its length and width a      Log On


   

Question 890126: The length of a rectangular parking lot is 36m longer than its width. The area of the parking lot is 5,152m2. If the area of the parking lot is double, would its length and width also double?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Original length and width, L and w.

L=w+36.
wL=w%28w%2B36%29=5152.
w%5E2%2B36w-5152=0
5152=4*4*2*161.
Discrim, 36^2-4*(-5152)=36+4*5152=21904, which is 148%5E2.
w=%28-36%2B148%29%2F2---using general solution of quadratic equation
highlight%28w=56%29
highlight%28L=92%29


Double the area.
Let the unknown distances increase by factor x .
%28w%2Ax%2ALx%29=2%2A5152, what is x ?
wL%2Ax%5E2=2%2A5152, we already know wL=5152.
x^2=2
highlight_green%28x=sqrt%282%29%29----this is not doubled.

...would its length and width also double? No.