Question

A right triangle's height is 3 times the length of its base. if the area of the triangle is 486, what is the height?

Answer 1

The formula of the area of a triangle:
$A_\Delta=\dfrac{bh}{2}$
b - the bash - the height
We have:
b - the base3b - the height486 - the area

Substitute:
$\dfrac{3b\cdot b}{2}=486\ \ \ |\cdot2\\\\3b^2=972\ \ \ |:3\\\\b^2=324\to b=\sqrt{324}\\\\b=16\to h=3b=3\cdot18=54$
Answer: The length of the height is equal 54 units.