The area of a parallelogram is given by the formula A=bh
Area = Base * height
Given Area = 91 square units
Base = 3x+1
height = x+1
Plug it in the formula
A= base * height
91 = (3x+1)(x+1)
Now we FOIL (3x+1)(x+1)
91 = 3x^2 +1x + 3x + 1
[tex]91 = 3x^2 + 4x + 1[/tex]
Now we subtract 91 on both sides
[tex] 0 = 3x^2 + 4x -90[/tex]
Now we solve for x using quadratic formula
a=3, b=4, c=-90
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2}[/tex]
[tex]x = \frac{-4+-\sqrt{4^2-4*(3)(-90)}}{2(3)}[/tex]
When we simplify it we will get two values for x
[tex]x=\frac{-2-\sqrt{274}}{3}[/tex] and [tex]x=\frac{-2+\sqrt{274}}{3}[/tex]
so x= 4.85 and x=-6.1 , base and height cannot be negative so we ignore negative value
x= 4.85
Base = 3x+1 = 3(4.85) + 1= 15.55
Height = x+1 = 4.85 + 1 = 5.85
so Base = 15.55 units and height = 5.85 units
