Find the base and height of the triangle

The height of a triangle is 3 m more than twice the length of the base. The area of the triangle is 45 m². 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 + 3 = height {the height is three more than twice the base}

45 = (1/2)(b)(2b + 3) {substituted base and height into area formula}
90 = b(2b + 3) {multiplied each side by 2}
90 = 2b² + 3b {used distributive property}
2b² + 3b - 90 = 0 {subtracted 90 from each side}
2b² + 15b - 12b - 90 = 0 {split 3b into two terms, whose product is -180 and whose sum is 3}
b(2b + 15) - 6(2b + 15) = 0 {factored out common factor from first two terms and last two terms}
(2b + 15)(b - 6) = 0 {factored (2b + 15) out of the two terms}
2b + 15 = 0 or b - 6 = 0 {set each factor equal to zero}
b = -15/2 or b = 6 {solved each equation}

b = 6 {base cannot be negative}
2b + 3 = 15 {substituted 6, in for b, into 2b + 3}

base = 6 m
height = 15 m

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