Question

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?

Answer 1

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