Question

The base of an isosceles triangle has length 12. What can you say about the length of a leg?

Short answer

Leg of the isosceles triangle must have length in between 6 and 18.

Step-by-step solution

Step 1. Apply the concept of isosceles triangle.

An isosceles triangle is a triangle that has two sides of equal length.

Any leg of a triangle must be less than the sum of two sides of triangle.

Step 2. Step description.

Consider that an isosceles triangle ABC as below:

Draw a perpendicular from point A.

Thus, AD bisect the base BC.

$CD=6$

Thus, the leg of the isosceles triangle must be greater than 6.

Step 3. Step description.

Also, any leg of a triangle must be less than the sum of two sides of triangle.

Therefore,

$\begin{array}{l}AC<6+12\\ AC<18\end{array}$

Hence the leg of the isosceles triangle must be in between 6 and 18