Answer
Please see "work step-by-step" for full sample answer.
Work Step by Step
To check, take a value for x, such as x=4 ft.
(I take this value because one side is going to be 10 ft, and multiplying with 10 is easy)
Then, the dimensions of Kelly's plot are (10)$\times$(6), the area 60 f$t^{2}$.
Substituting x=4 into the polynomial $x^{2}+8x+12$,
which we arrived at in part (a),
$(4)^{2}+8(4)+12=16+32+12=60,$
we get the same area,
so it checks out well.
Do the same for Roberto's plot. Take x=4,
Dimensions: (10)$\times$(7), Area = 70.
Polynomial ($x^{2}+9x+18$) value when x=4:
$4^{2}+9(4)+18=16+36+18 = 70.... $
so, this is also OK.
