Find the height of the triangle.

Question

Triangle: The area of a triangle whose height is 6 less than 3 times its base is 36 cm². Find the height of the triangle. (A = 0.5bh)

Answer 1

Area = 1/2 * b* h

where:

b = base

h = height

since height = 3b - 6, then:

Area = 1/2 * b * (3b - 6)

since Area = 36:

36 = 1/2 * b * (3b - 6)

multiply both sides by 2:

72 = b * (3b - 6)

distribute:

72 = 3b^2 - 6b

subtract 72 from both sides of the equation:

3b^2 - 6b - 72 = 0

divide both sides of the equation by 3:

b^2 -2b - 24 = 0

factor:

(b - 6)(b + 4)

b = 6 or -4

since base cannot be negative, b = 6

h = 3*b - 6 = 3(6) - 6 = 12

Answer 2

h = 3b - 6

A = 36

Now substitute and solve for h