The base of a triangle is one-third as long as its height. If the area of the triangle is 54 square meters, how long is its base?

The area of a triangle is given by the formula b * h, where b is the base and h is the height.

We know that the base of the triangle is one third of the height.

Therefore the base = h/3

The area is 54 square metres.

h/3 * h / 2 = 54

gives

h^2/6 = 54

Multiply both sides by 6 to remove the denominator

h^2=324

h = square root of 324 = 18.

b = h/3

b = 18/3

b = 6