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Equation |x/2| + |y/2| = 5 encloses a certain region on the [#permalink]

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20 Dec 2005, 05:16

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Equation |x/2| + |y/2| = 5 encloses a certain region on the coordiante plane. What is the area of the region

A 20
B 50
C 100
D 200
E 400

The line of argument I use is insufficient, since it leads always to 100. Please give me an explanation other than that provided in the challenge. Thanks

Equation |x/2| + |y/2| = 5 encloses a certain region on the coordiante plane. What is the area of the region?

1) If x < 0 and y < 0, -(x/2)-(y/2)=5 ---> y = -x - 10
2) If x < 0 and y > 0, -(x/2)+(y/2)=5 ---> y = x + 10
3) If x > 0 and y < 0, (x/2)-(y/2)=5 ---> y = x - 10
4) If x > 0 and y > 0, (x/2)+(y/2)=5 ---> y = -x + 10

When we draw a graph using the above 4 equtations, we will have a square one of whose length is 10root2.

Equation |x/2| + |y/2| = 5 encloses a certain region on the coordiante plane. What is the area of the region?

1) If x < 0 and y < 0, -(x/2)-(y/2)=5 ---> y = -x - 10 2) If x < 0 and y > 0, -(x/2)+(y/2)=5 ---> y = x + 10 3) If x > 0 and y < 0, (x/2)-(y/2)=5 ---> y = x - 10 4) If x > 0 and y > 0, (x/2)+(y/2)=5 ---> y = -x + 10

When we draw a graph using the above 4 equtations, we will have a square one of whose length is 10root2.

10root2 * 10root2 = 200

I vote for (D) 200.

The first step is clear, but unfortunately the second step not. We have four ( three) equations, I see them infront of me, but why should the sides be 10sqrt2?

Equation |x/2| + |y/2| = 5 encloses a certain region on the coordiante plane. What is the area of the region?

1) If x < 0 and y < 0, -(x/2)-(y/2)=5 ---> y = -x - 10 2) If x < 0 and y > 0, -(x/2)+(y/2)=5 ---> y = x + 10 3) If x > 0 and y < 0, (x/2)-(y/2)=5 ---> y = x - 10 4) If x > 0 and y > 0, (x/2)+(y/2)=5 ---> y = -x + 10

When we draw a graph using the above 4 equtations, we will have a square one of whose length is 10root2.

10root2 * 10root2 = 200

I vote for (D) 200. The first step is clear, but unfortunately the second step not. We have four ( three) equations, I see them infront of me, but why should the sides be 10sqrt2?

It's the Pythagorean theorem. ( a^2 + b^2 = c^2 )

Or you can just simply think that there are 4 triangles.