Question

c = left side of triangle
8 mi = right side of triangle
2 mi = bottom of triangle
What is the perimeter? If necessary, round to the nearest tenth.
miles

Answer 1

To find the perimeter of the triangle, we need to determine the length of the left side (c) along with the lengths of the other two sides, which are given as:

- Right side = 8 mi
- Bottom side = 2 mi

We can use the Pythagorean theorem to find \( c \) (the left side of the triangle), assuming the triangle is a right triangle. The Pythagorean theorem states that:

\[
c^2 = a^2 + b^2
\]

where \( a \) and \( b \) are the lengths of the two legs of the right triangle. In this case:

- \( a = 2 \) mi (bottom side)
- \( b = 8 \) mi (right side)

Now, we can substitute in the values:

\[
c^2 = 2^2 + 8^2
\]
\[
c^2 = 4 + 64
\]
\[
c^2 = 68
\]
\[
c = \sqrt{68} \approx 8.2462 \text{ mi}
\]

Next, we can calculate the perimeter (P) of the triangle:

\[
P = a + b + c = 2 + 8 + \sqrt{68}
\]

Since \( \sqrt{68} \approx 8.2462 \), the perimeter will be:

\[
P \approx 2 + 8 + 8.2462 \approx 18.2462 \text{ mi}
\]

Rounding to the nearest tenth:

\[
P \approx 18.2 \text{ mi}
\]

So, the perimeter of the triangle is approximately **18.2 miles**.