Chapter 5, Problem 14A

Interpretation Introduction

Interpretation: A man is $1.62\text{m}$ tall or a woman is $5\text{ft}\text{6}\text{in}\text{.}$ tall. Comparison of their height is needs to be explained.

Concept Introduction: Choose a conversion factor to convert from ft and in. to cm, which cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units. In case of conversion of ft to m, the conversion factor is $\frac{0.3048\text{m}}{1\text{ft}}$ . And conversion of in. to m, the conversion factor is $\frac{0.0254\text{m}}{1\text{in}}$ .

Answer to Problem 14A

According to the question, the height of the man is $1.62\text{m}$ but the woman’s height in m is $\text{1}\text{.68}\text{m}$ . Therefore, the woman is taller than the man.

Explanation of Solution

Height of both man and woman are given in different units one is given in ft in. and another one is in m.

Now, to compare their heights convert woman heights from ft. in to m (meter).

  $\begin{array}{c}\text{Height}\text{of}\text{woman}=5\text{ft}\text{6}\text{in}\text{.}\\ \text{=5}\text{ft}\times \frac{0.3048\text{m}}{1\text{ft}}+6\text{in}\times \frac{0.0254\text{m}}{1\text{in}}\\ =1.524\text{m+0}\text{.152}\text{m}\\ \text{=1}\text{.68}\text{m}\end{array}$

Hence, the height of the woman in m is $\text{1}\text{.68}\text{m}$ .

The height of the man is $1.62\text{m}$ but the height of the woman is $\text{1}\text{.68}\text{m}$ . Therefore, the woman is taller than the man.

Conclusion

According to question, the height of the man is $1.62\text{m}$ but the woman’s height in m is $\text{1}\text{.68}\text{m}$ . The height of woman is greater than the man. So, the woman is taller than the man.