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 14 and its height is 6?

Answer 1

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.