Question

find the perimeter. write your answer as a fraction or as a whole or mixed number.
3 7/10 cm
3 7/20 cm
2 19/20 cm
4 9/10 cm
box centimeters

Explanation:

Step1: Convert mixed numbers to improper fractions (or find common denominators)

First, let's list the side lengths: \( 3\frac{7}{10} \) cm, \( 2\frac{19}{20} \) cm, \( 4\frac{9}{10} \) cm, and \( 3\frac{7}{20} \) cm. To add them, we can convert to fractions with denominator 20.

\( 3\frac{7}{10} = 3 + \frac{7\times2}{10\times2} = 3\frac{14}{20} = \frac{3\times20 + 14}{20} = \frac{74}{20} \)

\( 2\frac{19}{20} = \frac{2\times20 + 19}{20} = \frac{59}{20} \)

\( 4\frac{9}{10} = 4 + \frac{9\times2}{10\times2} = 4\frac{18}{20} = \frac{4\times20 + 18}{20} = \frac{98}{20} \)

\( 3\frac{7}{20} = \frac{3\times20 + 7}{20} = \frac{67}{20} \)

Step2: Add all the side lengths

Perimeter \( P = \frac{74}{20} + \frac{59}{20} + \frac{98}{20} + \frac{67}{20} \)

Combine the numerators: \( 74 + 59 + 98 + 67 = 74 + 59 = 133; 133 + 98 = 231; 231 + 67 = 298 \)

So \( P = \frac{298}{20} \)

Step3: Simplify the fraction

Simplify \( \frac{298}{20} \): divide numerator and denominator by 2, we get \( \frac{149}{10} = 14\frac{9}{10} \) (or we can add the mixed numbers directly by adding whole parts and fractional parts separately)

Alternative way (adding mixed numbers directly):

Whole parts: \( 3 + 2 + 4 + 3 = 12 \)

Fractional parts: \( \frac{7}{10} + \frac{19}{20} + \frac{9}{10} + \frac{7}{20} \)

Convert \( \frac{7}{10} \) to \( \frac{14}{20} \) and \( \frac{9}{10} \) to \( \frac{18}{20} \)

Fractional sum: \( \frac{14}{20} + \frac{19}{20} + \frac{18}{20} + \frac{7}{20} = \frac{14 + 19 + 18 + 7}{20} = \frac{58}{20} = \frac{29}{10} = 2\frac{9}{10} \)

Total perimeter: \( 12 + 2\frac{9}{10} = 14\frac{9}{10} \)

Answer:

\( 14\frac{9}{10} \)