The area of a triangle varies directly with its height. A triangle with an area of 42 in² has a height of 6 inches. %0D%0A%0D%0AWhat is the area of the triangle when the height is 11 inches?
First, we need to determine the constant of variation between the area and the height of the triangle. We can do this by using the given information that a triangle with an area of 42 in² has a height of 6 inches.
Let A be the area of the triangle and H be the height. Then, we have:
A = kH
42 = k * 6
k = 7
Now that we have the constant of variation, we can calculate the area of the triangle when the height is 11 inches:
A = 7 * 11
A = 77
Therefore, the area of the triangle when the height is 11 inches is 77 in².