### Brain Teasers

# Triangle sizes

Which triangle has the most area? Is it

one with sides measuring:

A) 23 in., 20 in., & 10 in.

B) 2 in., 3 in., & 5 in.

C) 15 in. 7 in., & 22 in.

one with sides measuring:

A) 23 in., 20 in., & 10 in.

B) 2 in., 3 in., & 5 in.

C) 15 in. 7 in., & 22 in.

### Answer

A is the largest. B & C don't formtriangles! Those sides can only form a

line. A is the only real triangle.

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## Comments

What the heck?

Any three lines can make a triangle no matter their size.

If you were talking about a "right-angled triangle" or an "isoceles triangle" or an "equilateral triangle", then yes there are restrictions.

In this case, no. Not a fun question or answer.

Any three lines can make a triangle no matter their size.

If you were talking about a "right-angled triangle" or an "isoceles triangle" or an "equilateral triangle", then yes there are restrictions.

In this case, no. Not a fun question or answer.

No sane, Mogmatt is right. Try it If you have a line segment of 5, then the shortest distance between the endpoints of the segment is 5. place a compass on one endpoint and draw a circle of radius 3, then go to the other endpoint and draw a circle of radius 2. The only place that the circles meet is on the line 5 units long. There would be no way to get the smaller segments to connect otherwise.

Mog is right, however this is more of a trick teaser than math.

It might be a bit of a trick, but I liked it very much. I'm pretty psyched I figured it out before I actually did the math.

At least if you're going to make a trick, you should make it SEEM like the answer could be one of the others. Since every side of the first one listed was longer than every side of the other two, I didn't even get to the point of seeing that the other two weren't triangles.

(While I realize that having every side longer doesn't mean the area is larger, there was nothing extreme about the dimensions of the first triangle that would make it small enough for there to be a chance of either of the others being larger.)

(While I realize that having every side longer doesn't mean the area is larger, there was nothing extreme about the dimensions of the first triangle that would make it small enough for there to be a chance of either of the others being larger.)

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