The length of an altitude of a triangle is 1/3 the length of the side to which it is drawn. If the area is 6 square cm., then what is the length of the altitude?
h= altitude
A = 1/2 b * h
h = 1/3b
6 = 1/2b * 1/3b
Solve for b then for h.
To solve this problem, we can use the formula for the area of a triangle. The area of a triangle is given by the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is the side to which the altitude is drawn and the height of the triangle is the altitude itself.
We are given that the area of the triangle is 6 square cm. So we can write the equation as:
6 = (1/2) * base * altitude
Now, we are also given that the length of the altitude is 1/3 the length of the side to which it is drawn. Let's represent the length of the side to which the altitude is drawn as x. Then we can write the length of the altitude as (1/3) * x.
Substituting the values into the equation, we have:
6 = (1/2) * x * (1/3) * x
Simplifying, we get:
6 = (1/6) * x^2
Multiplying both sides of the equation by 6, we have:
36 = x^2
Taking the square root of both sides, we get:
6 = x
So the length of the side to which the altitude is drawn is 6 cm. And since the length of the altitude is 1/3 the length of the side, the length of the altitude is (1/3) * 6 = 2 cm.
Therefore, the length of the altitude of the triangle is 2 cm.