## imqwerty one year ago Hi ppl

1. Study_together

2. anonymous

Hi ^-^ have a question ? :)

3. imqwerty

Wait m sending it

4. Study_together

^_^

5. imqwerty

Jst one min

6. imqwerty

7. imqwerty

@ganeshie8 @Study_together @Moe95

I think you mean *People

9. imqwerty

10. anonymous

Do P and Q have to be adjacent?

11. imqwerty

yes P and Q have to be adjacent

12. anonymous

Let AC be represented by $$y_1=\frac43x_1$$ and let CB be represented by $$y_2=-\frac34x_2+\frac{15}{4}$$ on the specified intervals. (I skipped a few of the geometry steps, but basically, it looks like:) |dw:1437066809049:dw| We want to minimize the quantity $$y_1^2+y_2^2$$ since that represents the sum of the areas. Our constraint is that the distance on the x-axis must correspond to 5 since it's a right triangle. So, I set up a constraint function. $x_1+y_1+y_2+(5-x_2)=5$$\implies28x_1-21x_2=-45$$\implies x_1=\frac{21x_2-45}{28}$Substituting in, we get $$y_1$$ in terms of $$x_2$$$y_1=x_2-\frac{15}{7}$NOTE: I kind of assumed that the constraint function will make P and Q adjacent because it logically makes sense to me. I double check later that it is the case.Substituting in all of this into $$A=y_1^2+y_2^2$$, we get$A=\frac{25}{16}x_2^2-\frac{555}{56}x_2+\frac{14625}{784}$Now, we find the minimum by finding the vertex or by using calc.$0=\frac{25}{8}x_2-\frac{555}{56}$$x_2=\frac{111}{35}$We know this is the minimum value based on the fact that it's a parabola. Plugging everything back in, we get $(x_1,y_1)=\left(\frac{27}{35},\frac{36}{35}\right)$$(x_2,y_2)=\left(\frac{111}{35},\frac{48}{35}\right)$And because $$x_2-x_1=y_2+y_1$$, we have confirmed that P and Q are adjacent to each other. Plugging in $$x_2$$ back into $$A$$, we get $$A=\frac{144}{49}$$That was my solution. I probably did it the stupid hard way; there's probably an easier Geometry solution.

13. imqwerty

@dan815

14. dan815

ah this one is a special triangle so

15. dan815

|dw:1437071838075:dw|

16. imqwerty

yes we need to find the min. possible area of the 2 adjacent squares

17. dan815

|dw:1437072585380:dw|