The height of a triangle is four times the length of the base find the base and height of the triangle if the base is 18 square inches?

18 square inches is probably the area of the triangle, not the length of the base. The length of the base would be measured in inches (a unit of length), not square inches (a unit of area).

So area = 1 / 2 * base * height = 18 square inches (given)

height = 4 * base (given)

1 / 2 * base * 4 * base = 18 square inches

2 * base * base = 18 square inches

base * base = 9 square inches

base = 3 inches

height = 4 * base = 4 * 3 inches = 12 inches

Checking our work:

height is 4 times the base (12 = 4 * 3)

area is 18 (1/2 * 12 * 3).