Chapter 7.6, Problem 3CYU

To determine

Check whether the table tennis table a dilation of atennis court or not and find the scale factor.

Answer to Problem 3CYU

The table tennis table is not a dilation of a tennis court.

Explanation of Solution

Given:

The given statement is that the dimensions of tennis court are $27$ feet by $78$ feet and the dimensions of a table tennis table are $152.5$ cm by $274$ cm.

  

Calculation:

Find the ratio of the length (the length of table tennis table and the length of tennis court)

Ratio (length) $=\frac{274\text{cm}}{78\text{ft}}=\frac{274\times 0.0328084\text{ft}}{78\text{ft}}=\frac{8.9895\text{ft}}{78\text{ft}}=0.11525$

Find the ratio of the width (the width of table tennis table and the width of tennis court)

Ratio (width) $=\frac{152.5\text{cm}}{27\text{ft}}=\frac{152.5\times 0.0328084\text{ft}}{27\text{ft}}=\frac{5.0032808\text{ft}}{27\text{ft}}=0.1853$

Now,

Ratio (length) $\ne$ Ratio (width)

Hence the table tennis table is not a dilation of a tennis court.