Find the base and height of the triangle

The height of a triangle is 2m more than twice the length of the base. The area of the triangle is 20m². Find the height of the triangle and the length of the base.

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​Area of a triangle = (1/2)(base)(height)

b = base
2b + 2 = height {the height is two more than twice the base}

20 = (1/2)(b)(2b + 2) {substituted base and height into area formula}
40 = b(2b + 2) {multiplied each side by 2}
40 = 2b² + 2b {used distributive property}
2b² + 2b - 40 = 0 {subtracted 40 from each side}
2(b² + b - 20) = 0   {factored 2 out}
b² + b - 20 = 0   {divided each side by 2}
(b + 5)(b - 4) = 0   {factored into two binomials}
b + 5 = 0   or   b - 4 = 0   {set each factor equal to zero}
b = -5   or   b = 4   {solved each equation}

b = 4   {base cannot be negative
2b + 2 = 10   {substituted 4, in for b, into 2b + 2}

base = 4 m
height = 10 m

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