a rectangular sheet of paper is folded in half, with the crease parallel to the shorter edge. it happens that the ratio of longer side to shorter side remains unchanged. what is this ratio? answer this and explain how u got the answer.. PLEASE??!
when the x by y sheet (y being the long side) is folded in half, the new dimensions are x by y/2.
y/x = x/(y/2)
y^2/2 = x^2
y^2/x^2 = 2
y/x = √2
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To find the ratio of the longer side to the shorter side after the paper is folded in half, let's first assign variables to the lengths of the sides of the rectangular sheet of paper.
Let the length of the longer side be 'L', and the length of the shorter side be 'S'.
After folding the paper in half, the longer side will become the shorter side of the folded paper. Therefore, let's say the length of the shorter side of the folded paper is 'S'.
Since the ratio of longer side to shorter side remains unchanged, we can write the following equation:
L / S = S / S
Simplifying this equation, we get:
L / S = 1
Now, we need to solve for L. Multiply both sides of the equation by S to isolate L:
L = S * 1
L = S
Thus, the ratio of the longer side (L) to the shorter side (S) after the paper is folded in half is 1:1, or simply 1.
In other words, the longer side becomes equal to the shorter side after folding the paper.
To find the ratio of the longer side to the shorter side in this scenario, we can use some basic geometry principles.
Let's assume the longer side of the rectangular sheet of paper is represented by length L and the shorter side is represented by length S.
When the rectangular sheet is folded in half, the length L will remain the same because the crease is parallel to the shorter side. The crease divides the longer side into two equal halves. So, we can say that after folding, the folded side will have length L/2.
Since the ratio of the longer side to the shorter side remains unchanged, we can set up the following equation:
L/S = (L/2)/S
To determine the ratio, we can cross-multiply the equation:
L * S = L * (L/2)
Simplifying the equation, we get:
S = L/2
Now, let's substitute this value of S into the equation to find the ratio:
L/S = L/(L/2)
We can simplify this by dividing L by (L/2):
L/S = (2L)/L
Simplifying further:
L/S = 2
So, the ratio of the longer side (L) to the shorter side (S) is 2:1.