Question

1. drawing conclusions in table tennis, the table is a rectangle 9 feet long and 5 feet wide. a tennis court is a rectangle 78 feet long and 36 feet wide. are the two surfaces similar? explain. if so, find the scale factor of the tennis court to the table.

Explanation:

Step1: Calculate the ratio of lengths

The length of the tennis - court is \(l_1 = 78\) feet and the length of the table - tennis table is \(l_2=9\) feet. The ratio of lengths is \(\frac{l_1}{l_2}=\frac{78}{9}=\frac{26}{3}\)

Step2: Calculate the ratio of widths

The width of the tennis - court is \(w_1 = 36\) feet and the width of the table - tennis table is \(w_2 = 5\) feet. The ratio of widths is \(\frac{w_1}{w_2}=\frac{36}{5}\)

Step3: Check for similarity

For two rectangles to be similar, the ratios of their corresponding sides must be equal. Since \(\frac{26}{3}
eq\frac{36}{5}\) (because \(26\times5=130\) and \(3\times36 = 108\)), the two rectangles (table - tennis table and tennis court) are not similar.

Answer:

The two surfaces (table - tennis table and tennis court) are not similar.