Q17. - Algebra 2

Question

A triangle has a base of length 17, and the other two sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?

Step-by-Step Solution

Answer

The shortest possible length of a side is 9. 

Step 1. Apply the properties of triangles

One of the properties of the triangle is sum of any two sides of the triangle is greater than the side of the triangle.

Step 2. Find two sides of the triangle

Consider the provided information.

A triangle has a base of length 17, and the other two sides are equal in length. 

Let the length of other two sides be x units each.

Step 3. Interpret third side of triangle

Now, sum of two sides of triangle is provided below.

$x+x=2x$

Recall that in a triangle sum of two sides is always greater than third side.

Therefore, the length of side with 17 units has to be less than 2x.

$\begin{array}{c}2x>17\\ x>\frac{17}{2}\\ x>8.5\end{array}$

Since, the lengths are integer values. The least possible integer value of x is 9.

Hence, the shortest possible length of a side is 9.