Answer:
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.
