# interesting problem but I need to solve it urgently help pl

#### dhillon

Hi, I need to solve this problem urgently. I need to hand this in tomorrow, so if by any chance someone has been able to work this out, please tell me; thank you.

Prove that if five points are drawn in a rectangle of dimensions 6cm by 8cm, then there exists a pair of points which are no more than 5cm apart. The hint for this question is to split the rectangle into four equal parts.

#### aswoods

Re: interesting problem but I need to solve it urgently hel

Quarter the rectangle into four 3x4 rectangles.

If you plot five points, at least two must be in the same quarter of the rectangle. But by Pythagoras's theorem, the opposite corners of any of the little rectangles are ... how far away from each other?

#### dhillon

Re: interesting problem but I need to solve it urgently help

Hey, sorry I'm not sure what you mean; could you please explain a little more? Thank you.

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#### MarkFL

Re: interesting pproblem but i need to solve it urgently hel

If you have a rectangle that measures 3 cm by 4 cm, what is the length of its diagonal, using the Pythagorean theorem?

#### The Chaz

Forum Staff
Re: interesting problem but I need to solve it urgently help

dhillon said:
Hey, sorry I'm not sure what you mean; could you please explain a little more? Thank you.
Could you please explain more about what you don't understand? aswoods's explanation was good.
Did you not understand why there must be a quadrant (quarter) of the original rectangle that contains two points?
What work have you done?
Do you know the Pythagorean theorem? Do you know how to find the length of the hypotenuse of a right triangle with sides 3 and 4?

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#### Eminem_Recovery

Re: interesting problem but I need to solve it urgently help

The Chaz said:
dhillon said:
Hey, sorry I'm not sure what you mean; could you please explain a little more? Thank you.
Could you please explain more about what you don't understand? aswoods's explanation was good.
Did you not understand why there must be a quadrant (quarter) of the original rectangle that contains two points?
What work have you done?
Do you know the Pythagorean theorem? Do you know how to find the length of the hypotenuse of a right triangle with sides 3 and 4?
Totally agree. Do you know Pythagoras's Theorem?

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#### dhillon

Re: interesting problem but I need to solve it urgently help

Oh I get you, sorry I'm a bit overtired, only had 2 hours sleep over the last 2 days, I'm soo stressed out, thanks again and sorry about that, so would there not be 4 pairs of solutions to the question, I thought there was only supposed to be a 'pair of point which are no more than 5cm apart', thanks once again.

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