The base of a triangle is 3 times its height. The area of the triangle is 92 square feet. If h represents the height of the triangle, write an equation that would find the height of the triangle.
A) $92 = h ( 3 h )$
B) $92 = \frac { 1 } { 2 } h ( 3 h )$
C) $92 = \frac { 1 } { 2 } \left( \frac { h } { 3 } \right) ( h )$
D) $92 = 2 h + 2 ( 3 h )$

Question

Quizplus · Accepted Answer

The equation for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the base, and h is the height. We are given that the base is 3 times the height, so b = 3h. We are also given that the area is 92, so we can substitute these values into the equation to get:
92 = 1/2 * (3h) * h
Simplifying this equation gives us:
92 = 3/2 * h^2
Dividing both sides by 3/2 gives us:
h^2 = (2/3) * 92
Taking the square root of both sides gives us:
h = sqrt[(2/3) * 92] = sqrt(184/3) = (2/3) * sqrt(69) 
This is the height of the triangle, and it matches the equation in choice B, which is therefore the correct answer.

The Base of a Triangle Is 3 Times Its Height 92=h(3h)92 = h ( 3 h )92=h(3h)

The Base of a Triangle Is 3 Times Its Height $92 = h ( 3 h )$