Chapter 6.4, Problem 31E

To determine

To calculate: If the table cloth is similar to the surface of the table.

Answer to Problem 31E

The table cloth is not similar to the surface of the table

Explanation of Solution

Given information:

Dimensions of rectangular table = $5\text{ foot by }3\text{ foot}$

The table cloth extends $\text{1 foot}$ beyond the table’s surface on each side.

Calculation:

To find if the table cloth is similar to the surface of the table, find the dimensions of the table cloth and then find the ratio of the side lengths of the corresponding sides of the table cloth and table surface. If they are equal, the table cloth and the table surface are similar.

Length of table cloth = $\text{1+1+5=7 foot}$

Width of table cloth = $\text{1+1+3=5 foot}$

Ratio of the corresponding side length=

  $\begin{array}{l}\frac{\text{Length of table cloth}}{\text{Length of table surface}}\underset{\_}{?}\frac{\text{Width of table cloth}}{\text{Width of table surface}}\text{ [Write proportion]}\\ \frac{7}{5}\underset{\_}{?}\frac{5}{3}\text{ [Substitute values]}\\ \text{ 7}\cdot 3\underset{\_}{?}5\cdot 5\text{ [Form cross product]}\\ \text{ 21}\ne 25\text{ [Multiply]}\end{array}$