Answer:
a. Perimeter of the tennis court = 6x + 12
Perimeter of the Basketball court = 7x + 36
b. x + 24
c. Length of the tennis court = 78 feet
Width of the tennis court = 36 feet
Length of the Basketball court = 94 feet
Width of the Basketball court = 50 feet
Step-by-step explanation:
a. Perimeter of the rectangle = 2(length + width)
So, perimeter of the tennis court = 2[(2x + 6) + x]
= 2(3x + 6)
= 6x + 12
Perimeter of the Basketball court = 2[(3x - 14)+([tex]\frac{1}{2}[/tex]x + 32)]
= 6x - 28 + x + 64
= 7x + 36
b. Perimeter of the Basketball court - perimeter of the tennis court
= (7x + 36) - (6x + 12)
= 7x + 36 - 6x - 12
= x + 24
So, perimeter of the basketball court is x + 24 feet greater than that of the tennis court
c. It is given that the width of the tennis court = 36 feet
But, from the figure,
width of the tennis court = x
So, x = 36
Therefore, length of the tennis court = 2x + 6
= 2(36) + 6
= 72 + 6
= 78 feet
Width of the tennis court = x = 36 feet
Length of the basketball court = 3x - 14
= 3(36) - 14
= 108 - 14
= 94 feet
Width of the basketball court = [tex]\frac{1}{2} x+32[/tex]
[tex]=\frac{1}{2} (36)+32[/tex]
= 18 + 32
= 50 feet
