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{the height is two more than twice the base}2b + 2 = height 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 mheight = 10 m Ask the House
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