SOLUTION: Please help me from this question ( one rectangle is ( 2x+1 ) units wide and ( 4+x ) units long. A second rectangle has a with of (x+9)units and length of (x+9) units. A. Which ha

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me from this question ( one rectangle is ( 2x+1 ) units wide and ( 4+x ) units long. A second rectangle has a with of (x+9)units and length of (x+9) units. A. Which ha      Log On


   

Question 975025: Please help me from this question ( one rectangle is ( 2x+1 ) units wide and ( 4+x ) units long. A second rectangle has a with of (x+9)units and length of (x+9) units.
A. Which has the greater area?
B. How much greater?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(2x+1)(x+4) and (x+9)(x+9) areas of two rectangles.
2x%5E2%2B9x%2B4 and x%5E2%2B18x%2B81, their areas.

Which area is greater?

Could the areas be equal?
2x%5E2%2B9x%2B4-x%5E2-18x-81=0
x%5E2-9x-77=0
Discriminant, 81+4*77=389, a POSITIVE prime number.

Could the areas be unequal? Yes. Which rectangle has greater area depends on x, which is still a variable.
graph%28300%2C300%2C+-30%2C30%2C-30%2C30%2Cx%5E2-9x-77%29

How much greater is one rectangle than the other?
Again, this is variable, depending on x, as long as x is not either root in the "equal" equation. The best you can give for how much greater is abs%28x%5E2-9x-77%29. For x between the roots, the first rectangle is of lesser area; for x outside the interval bounding the roots, the first rectangle is of greater area.