Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6?
To find the possible base and height of the second triangle, we can use the fact that the area of a triangle is given by the formula:
Area = 1/2 * base * height
Since the area of the two triangles is the same, we can set up the following equation:
1/2 * 14 * 6 = 1/2 * x * y
Simplifying this equation, we get:
42 = x * y
Since the base and height vary inversely, we can say that x = k/y, where k is a constant. Using this relationship, we can substitute x = k/y into the equation above:
42 = k
Therefore, the possible base and height of the second triangle are 42 and 1, respectively.