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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.
12 congruent individual plots
8ydx7=56yd 18ydx3=54yd
56yd+54yd=110yd
Total length: 110yd
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6 congruent congruent rectangles
4ydx2=8yd 3ydx2=6yd
8ydx4=32yd 6ydx3=18yd
18ydx3=54yd
32yd+54yd=86yd
Total length: 86yd
To find the total length of rope used in the first scenario, where the garden is sectioned off into 12 congruent individual plots, you'll need to calculate the perimeter of one plot and then multiply it by 12.
Looking at the diagram, you can see that each plot has a length of 3 yards and a width of 4 yards. To find the perimeter of one plot, you need to add up the lengths of all four sides.
In this case, two opposite sides have a length of 3 yards, and the other two opposite sides have a length of 4 yards. So the perimeter of one plot is 3 + 3 + 4 + 4 = 14 yards.
To find the total length of rope used to section off all 12 plots, you'll need to multiply the perimeter of one plot by 12. So the total length of rope used is 14 * 12 = 168 yards.
Now let's look at the second scenario, where the garden is sectioned off into six congruent rectangles. To find the total length of rope needed, you'll first need to determine the dimensions of each rectangle.
To divide the garden into six congruent rectangles, you'll need to divide the original width of 4 yards into six equal sections. Each section will then become the width of one of the rectangles.
Since the original width is 4 yards, each rectangle will have a width of 4 / 6 = 2/3 yards.
The length of each rectangle remains the same as before, which is 3 yards.
To find the perimeter of one rectangle, you need to add up the lengths of all four sides. In this case, two opposite sides have a length of 2/3 yards, and the other two opposite sides have a length of 3 yards.
So the perimeter of one rectangle is 2/3 + 2/3 + 3 + 3 = 8/3 + 6 = 26/3 yards.
To find the total length of rope needed to section off all six rectangles, you'll need to multiply the perimeter of one rectangle by 6. So the total length of rope needed is (26/3) * 6 = 52 yards.
Therefore, in the second scenario where the garden is sectioned off into six congruent rectangles, you would need 52 yards of rope.