Question

find the perimeter. write your answer as a fraction or as a whole or mixed number. 1 2/3 km, 1 2/3 km, 3/4 km, 3/4 km

Explanation:

Step1: Convert mixed numbers to improper fractions

The mixed number \(1\frac{2}{3}\) can be converted to an improper fraction. To do this, we multiply the whole number part (1) by the denominator (3) and add the numerator (2). So, \(1\frac{2}{3}=\frac{1\times3 + 2}{3}=\frac{5}{3}\).

Step2: Identify the lengths of all sides

The quadrilateral has two sides of length \(1\frac{2}{3}\) km (which is \(\frac{5}{3}\) km) and two sides of length \(\frac{3}{4}\) km.

Step3: Calculate the sum of all sides

To find the perimeter, we add up all the side lengths. So, the perimeter \(P\) is:

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Simplify \(\frac{6}{4}\) to \(\frac{3}{2}\). Now we have:

$$ P = \frac{10}{3}+\frac{3}{2} $$

To add these fractions, we need a common denominator. The least common denominator of 3 and 2 is 6. Convert each fraction:

$$ \frac{10}{3}=\frac{10\times2}{3\times2}=\frac{20}{6} $$

$$ \frac{3}{2}=\frac{3\times3}{2\times3}=\frac{9}{6} $$

Now add the fractions:

$$ P=\frac{20}{6}+\frac{9}{6}=\frac{29}{6} $$

Convert \(\frac{29}{6}\) back to a mixed number: \(4\frac{5}{6}\) (since \(29\div6 = 4\) with a remainder of 5).

Answer:

\(4\frac{5}{6}\)