Question

The base of each triangle varies inversely with the height. what are the possible base is 14 and height of a second triangle if the first triangle's base is 14 and its height 6 is ?

Answer 1

The possible base and height of a second triangle are:

• B = 5
• H = 12

What is a triangle?

• A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry.
• Triangle ABC denotes a triangle with vertices A, B, and C.
• In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

To find the base and height of the triangle:

First, we 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.

When we clear "k", we obtain:

• B = k/H
• k = BxH
• k = 10x6
• k = 60

Now, we have:

• B = 60/H

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

If H = 12, then:

• B = 60/H
• B = 60/12
• B = 5

Therefore, the possible base and height of a second triangle are:

• B = 5
• H = 12

Know more about triangles here:

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