If equation encloses a certain region on the coordinate plane |x|+|y|=5, what is the area of that region?
5
10
25
50
100
area of that region
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|x|+|y|=5 represents four lines in the four quadrants
x+y=5
x-y=5
-x-y=5
x-y=0
forming a square with side 10.
Area = 100
x+y=5
x-y=5
-x-y=5
x-y=0
forming a square with side 10.
Area = 100
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IMO D (50)
You get four different equations:
1. y=-x+5
2. y=-x-5
3. y=x-5
4. y=x+5
These form a square with the y-axis as its diagonal of length 10.
This diagonal divides the square into two isoceles triangles of the form 45-45-90. The ratio of the sides in this kind of triangle is x : x : x*sqroot2.
Therefore x*sqroot2=10
x=10/sqroot2
Now we can solve for the area:
x^2=(10/sqroot2)^2=100/2=50
You get four different equations:
1. y=-x+5
2. y=-x-5
3. y=x-5
4. y=x+5
These form a square with the y-axis as its diagonal of length 10.
This diagonal divides the square into two isoceles triangles of the form 45-45-90. The ratio of the sides in this kind of triangle is x : x : x*sqroot2.
Therefore x*sqroot2=10
x=10/sqroot2
Now we can solve for the area:
x^2=(10/sqroot2)^2=100/2=50
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- Senior | Next Rank: 100 Posts
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