SOLUTION: Help! I don't know how to solve this! one rectangle is (2x + 3) units wide and (7x - 5) units long. A second rectangle has a width of (3x - 9) units and a length of (8x - 2) uni

Algebra ->  Rectangles -> SOLUTION: Help! I don't know how to solve this! one rectangle is (2x + 3) units wide and (7x - 5) units long. A second rectangle has a width of (3x - 9) units and a length of (8x - 2) uni      Log On


   

Question 363981: Help! I don't know how to solve this!
one rectangle is (2x + 3) units wide and (7x - 5) units long. A second rectangle has a width of (3x - 9) units and a length of (8x - 2) units. Which has the greater area? How much greater?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Rectangle 1: (2x+3)(7x-5)=14x^2+11x-15
Rectangle 2: (3x-9)(8x-2)=24x^2-78x+18
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14x^2+11x-15=0
x=-1.5, x=.714... Between x=-1.5 and x=.714 y is negative.
.
24x^2-78x+18=0
x=.25, x=3 Between x=.25 and x=3 y is negative.
.
24x^2-78x+18-(14x^2+11x-15)=10x^2-89x+33
10x^2-89x+33=0
x=.3877..., x=8.512...
For .25%3Cx%3C.714 both rectangles have a negative area.
For .714%3Cx%3C8.512 Rectangle 1 has a larger area than rectangle 2
For 0%3Cx%3C.25 and 8.512%3Cx%3Cinfinity rectangle 2 has a larger area than rectangle 1.
.
Ed