Question

1. two common envelope sizes are $3\frac{1}{2}$ in. $\times6\frac{1}{2}$ in. and 4 in. $\times9\frac{1}{2}$ in. are these envelopes similar? explain.

Explanation:

Step1: Convert mixed numbers to improper fractions

\(3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}\), \(6\frac{1}{2}=\frac{6\times2+1}{2}=\frac{13}{2}\), \(9\frac{1}{2}=\frac{9\times2 + 1}{2}=\frac{19}{2}\)

Step2: Calculate the ratios of the corresponding sides

Ratio of the first pair of sides: \(\frac{\frac{7}{2}}{4}=\frac{7}{2}\times\frac{1}{4}=\frac{7}{8}\)
Ratio of the second pair of sides: \(\frac{\frac{13}{2}}{\frac{19}{2}}=\frac{13}{19}\)

Step3: Compare the ratios

Since \(\frac{7}{8}=0.875\) and \(\frac{13}{19}\approx0.684\), \(\frac{7}{8}
eq\frac{13}{19}\)

Answer:

No, the envelopes are not similar. Because the ratios of their corresponding side - lengths are not equal.