Help! I have a math problem to work on and my brain is on strike!

[Blue_Chill]

what size squares can be constructed on a 5 by 5 geoboard or can be drawn on 5 by 5 dot paper so that the vertices of the squares are located on the pegs or dots? for example, can you construct a square whose area is one square unit? two sqaure units?


Could someone help me out and explain to me how to solve this?

[northzax]

1. are you looking for

all the different sizes that are possible? or the total number of squares you can draw?

[Ready4Change]

2. Draw it out and look at it.

My minds visual. That's the way I get my brain around things like this.

[Mairead]

3. If I understand the problem correctly, you're looking for the *size*

of the squares on a 5x5 matrix, right? Not the max number or anything?

if so, then (the dot is merely a space character to keep the browser from deleting multiple blanks) you can do 4 squares.

x x x x x
x . . . x
x . . . x
x . . . x
x x x x x

x x x x
x . . x
x . . x
x x x x

x x x
x . x
x x x

x x
x x

It's a 'fencepost' problem.

[qb]

4. Maybe I'm missing something but it sounds simple...

Assuming 5 by 5 means 5 dots by 5 dots (not 5 units by 5 units), you can construct squares that are 1, 2, 3 or 4 square units in area.

On edit I mean 1, 4, 9, or 16 square units in area.

[Spentastic]

5. Hard without visual

max size is 5*5 = 25 units square. 4*4, 3*3,2*2,1*1 all work.

edit

good point from others 5 dots (not units) give max of 4*4

[trotsky]

6. Don't forget diagonal / diamond squares

. . . . .
. . X . .
. X . X .
. . X . .
. . . . .

That one would have an area of 2.