.) An architect is building a model of a tennis court for a new client. On the model, the court is 6 inches wide and 13 inches long. An official tennis court is 36 feet wide. What is the length of a tennis court? The architect decides to build a larger model with a length of 26 inches. What is the width of the larger model?
l/36 = 13/6
l = 36(13/6) = 96 feet
Use the same approach in the second of this question.
oops, don't know how I got that 96
should have been 78 feet
To find the length of a tennis court, we need to determine the proportion between the dimensions of the model and the actual court.
First, we need to convert the width of the actual tennis court from feet to inches. Since there are 12 inches in a foot, the width is 36 feet * 12 inches per foot = 432 inches.
Now, let's set up a proportion:
Width of the model / Length of the model = Width of the tennis court / Length of the tennis court.
Plugging in the known values, we have:
6 inches / 13 inches = 432 inches / Length of the tennis court.
Simplifying the proportion, we can find the length of the tennis court:
Length of the tennis court = (13 inches * 432 inches) / 6 inches = 936 inches.
Therefore, the length of a tennis court is 936 inches.
For the second part of the question, we are given that the length of the larger model is 26 inches. We can use the same proportion we found earlier and solve for the width of the larger model.
Width of the larger model / Length of the larger model = Width of the tennis court / Length of the tennis court.
Plugging in the values, we have:
Width of the larger model / 26 inches = 432 inches / 936 inches.
Now, let's solve for the width of the larger model:
Width of the larger model = (26 inches * 432 inches) / 936 inches = 11.96 inches.
Rounded to two decimal places, the width of the larger model is approximately 11.96 inches.