The first thing we must do for this case, is to define a variable. We have then: w: width of the rectangle. By definition, the area of the rectangle is the product of the length by the width. We have then: [tex]A = (w) * (2w + 7)
[/tex] Substituting the value of the area we have: [tex]99 = (w) * (2w + 7)
[/tex] Rewriting the polynomial: [tex]2w ^ 2 + 7w - 99 = 0
[/tex] When factoring we have: [tex](w + 9) (2w-11) = 0
[/tex] Taking the positive root we have: [tex]2w-11 = 0
2w = 11
w = 11/2
w = 5.5 yd[/tex] Then, the length of the rectangle is: [tex]2w + 7 = 2 (5.5) + 7 = 11 + 7 = 18 yd
[/tex] Answer: the dimensions of the rectangle are: width = 5.5 yd Long = 18 yd
