Question

The area of a parallelogram is given by the formula A=bh. The area of the parallelogram is 91 sq. units. Find its base and height. base=3x+1 height=x+1

Answer 1

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

$91 = 3x^2 + 4x + 1$

Now we subtract 91 on both sides

$0 = 3x^2 + 4x -90$

Now we solve for x using quadratic formula

a=3, b=4, c=-90

$x=\frac{-b+-\sqrt{b^2-4ac}}{2}$

$x = \frac{-4+-\sqrt{4^2-4*(3)(-90)}}{2(3)}$

When we simplify it we will get two values for x

$x=\frac{-2-\sqrt{274}}{3}$  and $x=\frac{-2+\sqrt{274}}{3}$

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