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. 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 Ask the House
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January 2021
