Question

find the perimeter.
write your answer as a fraction or as a whole or mixed number.
3 1/12 cm
4 1/6 cm
4 1/6 cm
3 1/12 cm
centimeters
submit

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times (length + width) \). Here, the length is \( 4\frac{1}{6} \) cm and the width is \( 3\frac{1}{12} \) cm.

Step2: Convert mixed numbers to improper fractions

First, convert \( 4\frac{1}{6} \) to an improper fraction: \( 4\frac{1}{6}=\frac{4\times6 + 1}{6}=\frac{25}{6} \).
Then, convert \( 3\frac{1}{12} \) to an improper fraction: \( 3\frac{1}{12}=\frac{3\times12 + 1}{12}=\frac{37}{12} \).

Step3: Find a common denominator and add length and width

The common denominator of 6 and 12 is 12. So, \( \frac{25}{6}=\frac{25\times2}{6\times2}=\frac{50}{12} \).
Now, add the length and width: \( \frac{50}{12}+\frac{37}{12}=\frac{50 + 37}{12}=\frac{87}{12} \).

Step4: Multiply by 2 to get the perimeter

Multiply the sum by 2: \( P = 2\times\frac{87}{12}=\frac{87}{6} \).

Step5: Simplify the fraction

Simplify \( \frac{87}{6} \): divide numerator and denominator by 3, we get \( \frac{29}{2} \), which is \( 14\frac{1}{2} \).
(Alternatively, we can also calculate by adding all sides: \( 2\times4\frac{1}{6}+2\times3\frac{1}{12} \). Let's check that way:
\( 2\times4\frac{1}{6}=8\frac{2}{6}=8\frac{1}{3}=\frac{25}{3} \), \( 2\times3\frac{1}{12}=6\frac{2}{12}=6\frac{1}{6}=\frac{37}{6} \).
Convert \( \frac{25}{3} \) to sixths: \( \frac{50}{6} \), then \( \frac{50}{6}+\frac{37}{6}=\frac{87}{6}=\frac{29}{2}=14\frac{1}{2} \).)

Answer:

\( 14\frac{1}{2} \) (or \( \frac{29}{2} \))