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=(-b+-√(b^2-4ac))/(2)`

`x = (-4+-√(4^2-4*(3)(-90)))/(2(3))`

When we simplify it we will get two values for x

`x=(-2-√(274))/(3)` and
`x=(-2+√(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