The dimensions of a standard tennis court are 36 ft. 78 ft. with a net that is 3 ft. high in the center. The court is modified for players aged 10 and under such that the dimensions are 27 ft. x 60 ft., and the same

net is used. Use similarity to determine if the modified court is similar to the standard court.

Try to dilate the modified court to make it the same size as the standard court. The dilation factor for the

width is

. The dilation factor for the length is

. Based on similarity, the modified

court is similar to the standard court.

The dilation factor of the width is 3/4

The dilation factor of the length is 10/13

The standard court and the modified court are not similar

Step-by-step explanation:

The given dimension of a tennis courts are given as follows;

The width of the standard tennis court = 36 ft.

The length of the standard tennis court = 78 ft.

The height of the  net of the standard tennis court = 3 ft.

The width of the modified tennis court = 27 ft.

The length of the modified tennis court = 60 ft.

The height of the  net of the standard tennis court = 3 ft.

The dilation factor of the width = (Modified court width)/(Standard court width)

∴ The dilation factor of the width = (27 ft.)/(36 ft.) = 3/4

Therefore, the width of the modified court = 3/4 × The width of the standard court

∴ The dilation factor of the length = (60 ft.)/(78 ft.) = 10/13

Therefore, the length of the modified court = 10/13 × The length of the standard court

The dilation factor for the width is different from the dilation factor for the length and the net of both courts are of equal dimension, therefore, based on similarity theorem, both courts are not similar.

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step-by-step explanation: