Question

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?

Answer 1

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