Base and height of a triangle

Question

The area of a triangle is 42 sq. feet, the base is 3x+15 and the height is x+2, find the base and height.

Answer 1

Area of triangle = 1/2 * base * height

42 = 1/2 * (3x+15) * (x+2)

84 = (3x^2 + 21x + 30)

3x^2 + 21x - 54 = 0

x^2 + 7x - 18 = 0

(x + 9)(x - 2) = 0

x = -9 or x = 2

x cannot be -9 as this will make base or height < 0

so x = 2

base = 3x + 15 = 3*2 + 15 = 21

height = x + 2 = 2 + 2 = 4