imqwerty one year ago help

1. imqwerty

if the sum of 2 opposite sides and a diagonal of a quadrilateral is 20 and the area is 50cm^2 then find the length of other diagonal

2. imqwerty

@ganeshie8

3. freckles

Is this a for fun question?

4. imqwerty

Nope :) i don't knw the answer too

5. freckles

Oh okay. lol Is it okay I just share some of my thoughts? I don't know the answer or yet how to get the answer.

6. imqwerty

I know that this question is related to the chapter- solutions of triangles

7. imqwerty

And i've got 1 more difficult question

8. freckles

|dw:1436981758315:dw| like I know the area of this is $A=\frac{1}{2}d_1(p_2+p_1)$

9. freckles

though we could also look at the area in terms of the other diagonal

10. freckles

|dw:1436981915339:dw| and we could say the area of that same quadrilateral is $A=\frac{1}{2}d_2(p_3+p_4)$

11. freckles

now I guess we can make the assumption that they are talking about $DC+AB+d_1=20 \\ \text{ and we have both } 100=d_1(p_1+p_2) \text{ and } 100=d_2(p_3+p_4)$

12. freckles

but we still have a lot of unknowns

13. freckles

or maybe they are known just I don't know how to know them :p

14. mathmath333

|dw:1436983573101:dw|

15. mathmath333

\large \color{black}{\begin{align} &a+c+e=20,\hspace{.33em}\\~\\ &e>a,e>b,e>c,e>d,\hspace{.33em}\\~\\ &f>a,f>b,f>c,f>d,\hspace{.33em}\\~\\ &\frac{\sqrt{(a+d+e)(a+d-e)(a+e-d)(d+e-a)}}{4}+\hspace{.33em}\\~\\ &\frac{\sqrt{(b+c+e)(b+c-e)(b+e-c)(c+e-b)}}{4}=50\hspace{.33em}\\~\\~\\~\\~\\ &\frac{\sqrt{(d+c+f)(c+d-f)(d+f-c)(c+f-d)}}{4}+\hspace{.33em}\\~\\ &\frac{\sqrt{(b+a+f)(b+a-f)(a+f-b)(f+b-a)}}{4}=50\hspace{.33em}\\~\\ \end{align}} some might be useful relations.

16. freckles

@dan815 do you know how to do this one?

17. dan815

|dw:1437015008576:dw|

18. dan815

ah we gotta consider heights separetly this only onle true when a and b are parallel

19. dan815

|dw:1437015997569:dw|

20. dan815

|dw:1437016226537:dw|

21. freckles

if it was cyclic quadrilateral I wonder if it would be easier

22. freckles

|dw:1437016332900:dw| this probably wouldn't even help

23. freckles

like that is only if the quadrilateral is a cyclic