Answer:
A. 6X+12 and 7X+36 respectively
B. X+24
C. Dimensions are 36 feet × 78 feet and 50 feet × 94 feet respectively
Step-by-step explanation:
We are given,
Dimensions of the perimeter court is X and 2X+6.
Dimensions of the basketball court is [tex]\frac{X}{2}+32[/tex] and 3X-14.
Since, both the courts are similar to a rectangular base.
Moreover, the perimeter of a rectangle = 2(L+W)
Thus, perimeter of the tennis court = 2(X+2X+6) = 2(3X+6) = 6X+12
And, perimeter of the basketball court = [tex]2[(\frac{X}{2}+32)+(3X-14)][/tex] = [tex]2[3X+\frac{X}{2}+32-14][/tex] = [tex]2[\frac{7X}{2}+18][/tex] = 7X+36
So, the perimeters of tennis and basketball court are 6X+12 and 7X+36 respectively.
Now, Perimeter of Basketball Court - Perimeter of Tennis court = 7X+36 - 6X+12 = X + 24
Hence, the perimeter of basketball court is bigger than the tennis court by X+24
Further, the width of the tennis court is 36 feet i.e. X = 36.
So, length of the perimeter = 2X+6 = 2×36 + 6 = 78 feet.
Thus, dimensions of the tennis court are 36 feet × 78 feet.
Moreover, the dimensions of the basketball court are [tex]\frac{X}{2}+32[/tex] = tex]\frac{36}{2}+32[/tex] = 18+32 = 50 feet and 3X-14 = 3×36-14 = 108-14 = 94 feet.
Thus, dimensions of the basketball court are 50 feet × 94 feet.
