## eroshea 3 years ago a piece of cardboard has an area of 486 cm^2. a square of side 3cm is cut from each corner and an open box is made by turning up the ends and sides if the volume of the box formed is 756cm^3. what are the dimensions of the cardboard?

1. hartnn

drawing a figure will help, could u draw a figure of this ?

2. eroshea

|dw:1353637103770:dw|

3. hartnn

|dw:1353579949506:dw|

4. hartnn

volume = 3(x-6)(y-6) = 756

5. hartnn

can u solve those 2 equations ? xy=486 3(x-6)(y-6) = 756 ?

6. eroshea

cAN I DO the substitution method?

7. eroshea

x = 486/y then substitute to the second equation

8. hartnn

try it, if u go wrong, i'll help.... instead substitute xy=486 in 2nd equation

9. hartnn

u get xy term in 2nd equation

10. hartnn

and u'll be able to find x+y from 2nd equation...

11. eroshea

18y^2-810y+8748 very big numbers >.<

12. hartnn

y^2-45y+486

13. hartnn

if 18y^2-810y+8748 is correct... i have not checked that.

14. hartnn

y^2-45y+486 =0 is correct can u factor it ?

15. hartnn

hint : 18*27 = 486

16. hartnn

y^2-45y+486 =0 (y-18)(y-27)=0

17. hartnn

find y from here, then u also get 2 values of x then dimensions are x,y

18. eroshea

you're a very big help to me my friend. thanks a lot :)