Question

find the perimeter. write your answer as a fraction or as a whole or mixed number. \\(\frac{1}{5}\\) cm \\(\frac{4}{15}\\) cm \\(\frac{1}{5}\\) cm

Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter \( P \) of a triangle is the sum of the lengths of its three sides. If the sides are \( a \), \( b \), and \( c \), then \( P=a + b + c \).

Step2: Identify the lengths of the sides

From the triangle, the lengths of the sides are \( \frac{1}{5}\text{cm} \), \( \frac{1}{5}\text{cm} \), and \( \frac{4}{15}\text{cm} \).

Step3: Add the lengths of the sides

First, we need to add \( \frac{1}{5}+\frac{1}{5}+\frac{4}{15} \).
We know that \( \frac{1}{5}+\frac{1}{5}=\frac{1 + 1}{5}=\frac{2}{5} \).
Now we need to add \( \frac{2}{5}+\frac{4}{15} \). To add these fractions, we find a common denominator, which is 15.
Convert \( \frac{2}{5} \) to fifteenths: \( \frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15} \).
Now add \( \frac{6}{15}+\frac{4}{15}=\frac{6 + 4}{15}=\frac{10}{15} \).
Simplify \( \frac{10}{15} \) by dividing both the numerator and the denominator by 5: \( \frac{10\div5}{15\div5}=\frac{2}{3} \).

Answer:

The perimeter of the triangle is \( \frac{2}{3}\text{cm} \).