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by praky_rules » Sat Sep 12, 2009 9:34 am
|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
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by Nermal » Sat Sep 12, 2009 12:14 pm
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
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by praky_rules » Sat Sep 12, 2009 3:31 pm
oops..I agree
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