As seen from the figure , the space is of the shape of a rectangle.
To find the rope required to enclose the space needed , they will have to first determine the perimeter of the rectangular region.
The perimeter of rectangle is given by:
[tex] Perimeter=2(l+w) [/tex]
Where l is length and w is width of the rectangle.
We are given in the figure that length is 4 2/3 yards and width is 3 1/2 yards.
Let us first convert these mixed fraction to improper fractions first.
4 2/3 is (4*3+2)/3 that is 14/3
3 1/2 is (3*2+1)/2 that is 7/2
Now we plug these values in the formula for perimeter,
[tex] Perimeter=2(l+w) [/tex]
[tex] Perimeter=2(\frac{14}{3}+\frac{7}{2}) [/tex]
Now we find lcd of 3 and 2, which is 6
[tex] Perimeter=2(\frac{28}{6}+\frac{21}{6}) [/tex]
Adding,
[tex] Perimeter=2(\frac{49}{6}) [/tex]
Perimeter = 49/3 yards
Answer: The girls need rope measuring 49/3 yards or 16.33 yards to completely enclose their space.
