## AndrewKaiser333 one year ago A graphics printing company sells three different sizes of posters. They use all of a 36" by 36" posterboard and cut it into 3 pieces. The smallest is a square, and the largest one will have three times the area of the middle-sized one. What are the dimensions of the three sizes of posters?

1. anonymous

|dw:1441235439107:dw|

2. AndrewKaiser333

What formula would you use or method? and what would you use to check your work i want to know this will help me get ready for my test this is a practice test said my teacher and he wants me to answer this in that way so i know what is going on. so if you can help me understand how you got that i would be happy.

3. anonymous

Solve the following for x:$\frac{36 (36-x)}{(36-x) x}=3$x = 12$\left\{x^2,x (36-x),36 (36-x)\right\}\text{/.}\, x\to 12$$\{144,288,864\}$$\frac{864}{288}=3$$\text{Total}[\{144,288,864\}] = 1296$

4. AndrewKaiser333

how would you check it

5. anonymous

362^2 = 1296

6. AndrewKaiser333

thanks

7. anonymous

As an aside, the sketch is not drawn to reflect the final placements of the three areas.

8. anonymous

Thank you for the medal.

9. AndrewKaiser333

um one question can you simplify the solve for how you solved it? or do i have to leave it that way???

10. anonymous

$\frac{36 (36-x)}{(36-x) x}=3$ The 36-x terms divide out leaving$\frac{36}{x}=3$ 3x = 36 x = 12

11. AndrewKaiser333

thanks

12. anonymous

You bet.

13. AndrewKaiser333

and that is the solve not {x^2, x(36−x), 36(36−x)} /. x→12 {144,288,864} 864/288=3 Total [{144,288,864}]=1296 or is this the check?

14. AndrewKaiser333

if that is for the check is there a way to simplify this?

15. AndrewKaiser333

???

16. AndrewKaiser333

nvm i think i figured out a way to simplify it

17. anonymous

{ x^2, x(36−x), 36(36−x) } /. x→12 The above statement is a computaional request statement for the computer program, Mathematica v9. { x^2, x(36−x), 36(36−x) } is a 3 element list of the area expressions for the square, small rectangle and large rectangle respectively. /. x→12 is a command to Mathematica to replace each x in the list expression with the value 12, and then evaluate and simplify the results. When finished, Mathematica returns the numerical results as a new 3 element list as shown below: {144, 288, 864} You can verify the above by using pencil and paper and your knowledge of arithmetic. Timing [ { x^2, x(36−x), 36(36−x) } /. x→12 ]

18. anonymous

Timing is a way to calculate the elapsed time for Mathematica to process a statement. $\left\{0.027404,\left\{x^2,(36-x) x,36 (36-x)\right\}\text{/.}\, x\rightarrow 12\right\}$ 0.027404 is 27404 microseconds to parse the text, do the calculation and format and present the results on the CRT tube.