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October 21st, 2014, 03:47 AM  #1 
Member Joined: Jun 2013 Posts: 42 Thanks: 0  Please Solve this 4 EPIC Problems.... i couldn't solve it myself
Please Solve this 4 EPIC Problems.... i couldn't solve it myself 1.) Find the area of the rectangle 2.) Find the cost of roadway 3.) Find the perimeter of the rectangle 4.) Find the distance from 200m to the center and 200m along the circle. when the circle has radius of 600m. The problem seems easy at first glance, but it's actually hard when you try to solve it. I'll salute you if you can solve one of them. I can't even solve it myself Last edited by skipjack; November 2nd, 2014 at 03:35 AM. 
October 21st, 2014, 07:50 AM  #2 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  The third one is the easiest. It is 28 cm. 
October 21st, 2014, 08:15 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,161 Thanks: 734 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
First one is $\displaystyle 200cm^2$.

October 21st, 2014, 09:14 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
#2 Area of the roadway is $\displaystyle 300\sqrt{2} \, m^2$ $ 1500 per square meter ... really? 
October 21st, 2014, 09:32 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
last one ... $\displaystyle d = 200\sqrt{1312\cos\left(\frac{1}{3}\right)}$ 
October 21st, 2014, 03:29 PM  #6 
Member Joined: Jun 2013 Posts: 42 Thanks: 0 
can you please show your solutions...thank you ^^

October 21st, 2014, 03:32 PM  #7 
Member Joined: Jun 2013 Posts: 42 Thanks: 0 
The answer to #2 is actually 651500.00 so 300sqrt2 is wrong because I get 636396.1.. I don't know the solution how to get 651500.. please help..
Last edited by skipjack; November 2nd, 2014 at 05:17 AM. 
October 21st, 2014, 03:42 PM  #8 
Member Joined: Jun 2013 Posts: 42 Thanks: 0 
@prakhar:how did you get 28cm? 28 is in one of the choices. It might be correct. Please show your solution. @Benit13:how did you get 200 cm^2? Yes, 200cm^2 is one of the choices. It might be correct. Please show your solution. @skeeter:I think it's correct. How did you get d=200(1312cos(1/3))^0.5?? Thanks for everyone who helped ^^ Last edited by skipjack; November 2nd, 2014 at 06:01 AM. 
October 21st, 2014, 04:46 PM  #9 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600  arc length formula & law of cosines
Last edited by skipjack; November 2nd, 2014 at 05:23 AM. 
October 21st, 2014, 07:00 PM  #10 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
2nd problem, I made an incorrect assumption, so tried it again and determined Cost = 45000x Where x is the horizontal distance between the sides of the road. Using similar triangles and Pythagoras, I came up with the equation ... $\displaystyle \frac{10}{\sqrt{x^2100}}=\frac{30}{40x}$ Solved for x, but still got a cost less than what you say is the correct solution. Sorry. 

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