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 10 and its height is 6?

1. First, you must find the constant of variation (k). The problem indicates that the base of each triangle varies inversely with the height. So, this can be represented as below:

 B=k/H

 B is the base of the triangle (B=10).
 H is the height of the triangle (H=6).
 k is the constant of variation.

 2. When you clear "k", you obtain:

 B=k/H
 k=BxH
 k=10x6
 k=60

 3. Now, you have:

 B=60/H

 4. You can give any value to "H" and you will obtain the base of the second triangle.

 5. If H=12, then:

 B=60/H
 B=60/12
 B=5

 6. Therefore, the possible base and height of a second triangle is:

 B=5
 H=12