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.
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 Ask the House
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January 2021
