Question

write your answer as a fraction or as a whole or mixed number. (\frac{1}{5}) yd, (\frac{2}{15}) yd, (\frac{1}{5}) yd triangle image (square) yards

Explanation:

Step1: Convert to common denominator

To add the lengths, first convert \(\frac{1}{5}\) to fifteenths. \(\frac{1}{5}=\frac{3}{15}\) (since \(5\times3 = 15\), multiply numerator and denominator by 3).

Step2: Add the three sides

The sides are \(\frac{3}{15}\), \(\frac{3}{15}\), and \(\frac{2}{15}\). Add them: \(\frac{3}{15}+\frac{3}{15}+\frac{2}{15}=\frac{3 + 3+ 2}{15}=\frac{8}{15}\)? Wait, no, wait. Wait, the two sides of \(\frac{1}{5}\) each: \(\frac{1}{5}+\frac{1}{5}+\frac{2}{15}\). Let's recalculate. \(\frac{1}{5}=\frac{3}{15}\), so two of them: \(\frac{3}{15}+\frac{3}{15}=\frac{6}{15}\), then add \(\frac{2}{15}\): \(\frac{6}{15}+\frac{2}{15}=\frac{8}{15}\)? Wait, no, wait, the perimeter of a triangle is the sum of all three sides. So sides are \(\frac{1}{5}\), \(\frac{1}{5}\), and \(\frac{2}{15}\). So convert \(\frac{1}{5}\) to \(\frac{3}{15}\), so two sides: \(2\times\frac{3}{15}=\frac{6}{15}\), plus \(\frac{2}{15}\): \(\frac{6}{15}+\frac{2}{15}=\frac{8}{15}\)? Wait, no, wait, \(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\), then convert \(\frac{2}{5}\) to fifteenths: \(\frac{6}{15}\), then add \(\frac{2}{15}\): \(\frac{6}{15}+\frac{2}{15}=\frac{8}{15}\)? Wait, no, wait, \(\frac{1}{5}+\frac{1}{5}+\frac{2}{15}\). Let's do it step by step. \(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\). Then \(\frac{2}{5}+\frac{2}{15}\). Convert \(\frac{2}{5}\) to \(\frac{6}{15}\), so \(\frac{6}{15}+\frac{2}{15}=\frac{8}{15}\)? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, \(\frac{1}{5}\) is 3/15, so two sides: 3/15 + 3/15 = 6/15, plus 2/15 is 8/15? Wait, but let's check again. The three sides are \(\frac{1}{5}\) yd, \(\frac{1}{5}\) yd, and \(\frac{2}{15}\) yd. So perimeter \(P=\frac{1}{5}+\frac{1}{5}+\frac{2}{15}\). Combine the first two terms: \(\frac{1 + 1}{5}=\frac{2}{5}\). Now, convert \(\frac{2}{5}\) to fifteenths: multiply numerator and denominator by 3: \(\frac{2\times3}{5\times3}=\frac{6}{15}\). Now add \(\frac{2}{15}\): \(\frac{6}{15}+\frac{2}{15}=\frac{6 + 2}{15}=\frac{8}{15}\)? Wait, no, that's correct? Wait, 1/5 is 0.2, so two of them is 0.4, and 2/15 is approximately 0.1333, so total is 0.5333, and 8/15 is approximately 0.5333. So that's correct.

Answer:

\(\frac{8}{15}\)