If a triangle's height is 4 inches less than two times it's base, and has an area of 120 square inches. What is the height of the triangle?

I know it's 20 inches but i need to show how I found it, but the equation I used [120 = 1/2b(2b - 4)] doesn't turn out right.

I know it's 20 inches but i need to show how I found it, but the equation I used [120 = 1/2b(2b - 4)] doesn't turn out right.

Area of a triangle = (base x height)/2

"height is 4 inches less than two times its base"

{usually whatever comes after the word than is what you let x equal}

x = base

2x - 4 = height

x(2x - 4)

------------ = 120

2

2x2 - 4x = 240 {multiply both sides by 2 to clear fraction out}

2x2 - 4x - 240 = 0 {subtract 240 from both sides}

2(x2 - 2x - 120) = 0 {factor 2 out}

2(x + 10)(x - 12) = 0 {factor into 2 binomials}

x + 10 = 0 or x - 12 = 0 {set each factor equal to 0}

x = -10 or x = 12 {solve each equation for x}

-----x cannot be negative-----

x = 12

2x - 4 = 20 inches {the height}

- Algebra House

"height is 4 inches less than two times its base"

{usually whatever comes after the word than is what you let x equal}

x = base

2x - 4 = height

x(2x - 4)

------------ = 120

2

2x2 - 4x = 240 {multiply both sides by 2 to clear fraction out}

2x2 - 4x - 240 = 0 {subtract 240 from both sides}

2(x2 - 2x - 120) = 0 {factor 2 out}

2(x + 10)(x - 12) = 0 {factor into 2 binomials}

x + 10 = 0 or x - 12 = 0 {set each factor equal to 0}

x = -10 or x = 12 {solve each equation for x}

-----x cannot be negative-----

x = 12

2x - 4 = 20 inches {the height}

- Algebra House