Question

The isosceles triangle has two sides with the same length. The base is one-half the length of a side. The expression which represents the perimeter, the distance around the triangle, is s + s + one-half s. What is the value of this expression if s = 8?

A triangle with 2 sides with length s.

Answer 1

To find the perimeter of the isosceles triangle given the sides, we use the expression for the perimeter:

\[
P = s + s + \frac{1}{2}s.
\]

First, we can simplify that expression:

\[
P = 2s + \frac{1}{2}s.
\]

To combine the terms, we can convert \(2s\) into a fraction:

\[
2s = \frac{4}{2}s.
\]

Now we can rewrite the perimeter expression as:

\[
P = \frac{4}{2}s + \frac{1}{2}s = \frac{4 + 1}{2}s = \frac{5}{2}s.
\]

Next, we can substitute \(s = 8\) into the perimeter expression:

\[
P = \frac{5}{2} \cdot 8.
\]

Calculating this gives:

\[
P = \frac{5 \cdot 8}{2} = \frac{40}{2} = 20.
\]

Thus, the value of the perimeter when \(s = 8\) is:

\[
\boxed{20}.
\]