A square pen that is surrounded by a fence is divided into two rectangular
regions by adding a new fence that connects the midpoints of two opposite
sides. By what percent has the total length of fencing been increased?
I had 4 equal lengths each of length L1
I added one L1 so had total = 5 L1
total/original = 5/4 = 1 + 1/4
so added 1/4 or 25% of original length
houda
L2 = (5/4)L1 = 1.25
.25 * 100 = ?
can you please explain in detail? thanks.
To find the percentage increase in the total length of fencing, we need to compare the original length of fencing with the new length of fencing.
Let's assume the length of each side of the square pen is "x".
The original length of fencing is the perimeter of the outside square, which is 4x.
After adding the new fence that connects the midpoints of two opposite sides, we divide the square into two rectangular regions.
The new length of fencing can be calculated as the sum of the lengths of the two longer sides of the rectangular regions, plus the two shorter sides.
Each longer side of the rectangular region has a length of x, and each shorter side has a length of x/2.
So the new length of fencing is:
2(x) + 2(x/2) = 2x + x = 3x.
Now we can calculate the percentage increase in the total length of fencing.
The increase in length is 3x (new length) - 4x (original length) = -x.
To find the percentage increase, we divide the increase by the original length of 4x, and multiply by 100:
((-x)/4x) * 100 = -25%.
Therefore, the total length of fencing has been increased by -25%, which means it has decreased by 25%.