A parallelogram has an area of x2 + 9x - 36. a. What are expressions for the length and width of the parallelogram?
b. If x is an integer, what is the least possible value of x for a parallelogram
to exist? Explain.

Step-by-step explanation:

Please use " ^ " to indicate exponentiation:

A = x^2 + 9x - 36.  This factors into A = (x + 12)(x - 3).  We can assume that the length of the parallelogram is x + 12 and that the width is x - 3.

Note that if x = 3 the area becomes zero.  So:  x must be greater than 3, so that the (x - 3) factor is positive.

Example:  If x = 4, then the dimensions of the parallelogram are 4 + 12, or 16, and 4 - 3, or 1.  

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

answer: finding the extract measurements and knowing the points

step-by-step explanation: