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# please help...

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A rectangle measures 6 centimeters by 25 centimeters. The probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is $$\frac p q$$, where $$p$$ and $$q$$ are relatively prime positive whole numbers. What is the sum of $$p$$ and $$q$$?

Mar 13, 2021

### 1+0 Answers

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I AM NOT  totally  sure  about this one, TGO,  but it's an interesting problem......here's  my best attempt

Look at  the image  below  : Note  that  any point lying  within  triangles  ADE  and  BCF   will be CLOSER  to  a side of  6  than to  a side of 25

Each of  these triangles has  a base of 6  and a height of  3

So....their total  area is  6 * 3   =18

And the total area of  the rectangle  = 25 * 6  =150

So....the  region  that a point  could fall into and  be  closer to a  side of 25  than a side of 6 has an area of :  150   -18 =   132

So....  p  / q   =  132   /150   =  22 /  25

So..... p + q  =   22 + 25  = 47   Mar 13, 2021