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

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) (Show Source): You can put this solution on YOUR website!
(2x+1)(x+4) and (x+9)(x+9) areas of two rectangles.
and , their areas.

Which area is greater?

Could the areas be equal?

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.

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 . 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.
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