Question

find the perimeter.
write your answer as a fraction or as a whole or mixed number.
image of a rectangle with length 3 1/4 yd and width 2 1/5 yd
______ yards

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length}+\text{width}) \). Here, the length is \( 3\frac{1}{4} \) yd and the width is \( 2\frac{1}{5} \) yd.

Step2: Convert mixed numbers to improper fractions

First, convert \( 3\frac{1}{4} \) to an improper fraction: \( 3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4} \).
Then, convert \( 2\frac{1}{5} \) to an improper fraction: \( 2\frac{1}{5}=\frac{2\times5+1}{5}=\frac{11}{5} \).

Step3: Calculate the sum of length and width

Add the two improper fractions: \( \frac{13}{4}+\frac{11}{5} \). To add these, find a common denominator, which is \( 20 \).
\( \frac{13}{4}=\frac{13\times5}{4\times5}=\frac{65}{20} \) and \( \frac{11}{5}=\frac{11\times4}{5\times4}=\frac{44}{20} \).
So, \( \frac{65}{20}+\frac{44}{20}=\frac{65 + 44}{20}=\frac{109}{20} \).

Step4: Multiply by 2 to get the perimeter

Multiply the sum by 2: \( P = 2\times\frac{109}{20}=\frac{109}{10} \). Convert \( \frac{109}{10} \) to a mixed number: \( \frac{109}{10}=10\frac{9}{10} \).
(Alternatively, we can also calculate \( 2\times3\frac{1}{4}+2\times2\frac{1}{5} \):
\( 2\times3\frac{1}{4}=2\times\frac{13}{4}=\frac{13}{2}=6\frac{1}{2} \),
\( 2\times2\frac{1}{5}=2\times\frac{11}{5}=\frac{22}{5}=4\frac{2}{5} \),
Then add \( 6\frac{1}{2}+4\frac{2}{5} \). Convert to common denominator (10):
\( 6\frac{1}{2}=6\frac{5}{10} \), \( 4\frac{2}{5}=4\frac{4}{10} \),
\( 6\frac{5}{10}+4\frac{4}{10}=10\frac{9}{10} \).)

Answer:

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