A right triangle's height is 3 times the length of its base. if the area of the triangle is 864, what is the height?

The area of a triangle is a half times base times height.

A = 0.5bh

864 = (0.5) (b) (3b)

864 = 0.5 * 3b^2

1728 = 3b^2

576 = b^2

√576 = √b^2

24 = b

Since the triangle's height is 3 times the length of its base then, the height is 72.

If we check the area by multiplying all values ...

A = 0.5bh

864 = (0.5) (24) (72)

864 = 864

The height of 72 is the correct value