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
