The base of a triangle is 4cm greater than the height. The area is 30cm^2. find the height and the length of the base.
Area, A, = 1/2bh. Given: b = h + 4, A = 30 cm^2. 30 = 1/2bh. Substitute b = h + 4 for b and solve for h. 30 = 1/2(h + 4)h. Multiply both sides of the equation by 2 to eliminate the fraction. 60 = (h + 4)h. Distribute h. 60 = h^2 + 4h. [ Subtract 60 from both sides of the equation. 0 = h^2 + 4h - 60. Factor. 0 = (h + 10)(h - 6). Set each binomial equation equal to 0. h + 10 = 0. h = - 10. Can't be an answer as it is negative. h - 6 = 0. h = 6 cm. Answer for the height. Since the base, b, = h + 4, substitute h = 6 and solve for b. b = 6 + 4 = 10 cm. Answer for the base. ]
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