The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, which equation models this situation?
We must know that the are of the triangle is given by definition by A = (1/2) * (b) * (h) where b = base h = height Substituting the values A = (1/2) * (x) * (1 + 6x) A = (1/2) * (x + 6x ^ 2) Since the area is 13 then (1/2) * (x + 6x ^ 2) = 13 Clearing x we have 6x ^ 2 + x = 26 6x ^ 2 + x-26 = 0 (x-2) * (x + 13/6) = 0 As we look for the base of a triangle then x> 0 x = 2 answer the base is x = 2 6x ^ 2 + x = 26
