A community garden is sectioned off into 12 congruent individual plots with rope as shown in the diagram. Find the total length of rope used. Then find the total length of rope needed if the garden is sectioned off into six congruent rectangles.
width-4yd
length-3rd
To find the total length of rope used in the garden, we first need to find the perimeter of each individual plot and then add them up.
Given the width and length of each individual plot, we can calculate the perimeter using the formula:
Perimeter = 2 * (width + length)
In this case, the width is 4 yards and the length is 3 yards, so we have:
Perimeter = 2 * (4 + 3) = 2 * 7 = 14 yards
Since there are 12 individual plots, we need to multiply the perimeter of one plot by 12 to get the total length of rope used:
Total length of rope used = 14 yards * 12 = 168 yards
Now, let's calculate the total length of rope needed if the garden is sectioned off into six congruent rectangles.
If the garden is sectioned off into six congruent rectangles, we need to consider the perimeter of each rectangle instead of each individual plot.
Since the width remains the same at 4 yards, but the length is divided by 6, the length of each rectangle becomes 3/6 = 0.5 yards.
Now, we can calculate the perimeter of each rectangle using the same formula:
Perimeter = 2 * (width + length) = 2 * (4 + 0.5) = 2 * 4.5 = 9 yards
Since there are 6 rectangles, we need to multiply the perimeter of one rectangle by 6 to get the total length of rope needed:
Total length of rope needed = 9 yards * 6 = 54 yards