## anonymous one year ago Find the length of a side of rhombus ABCD if AE=6".

1. anonymous

|dw:1437452607189:dw|

2. mathstudent55

What do you know about the diagonals of a rhombus?

3. anonymous

4. anonymous

CB=2x

5. mathstudent55

Yes, the diagonals of a rhombus bisect each other, but there is another important property of the diagonals of a rhombus.

6. anonymous

What is the other property?

7. mathstudent55

The are perpendicular to each other.

8. mathstudent55

Also, all sides of a rhombus are congruent. |dw:1437453036000:dw|

9. mathstudent55

Now you can use the Pythagorean theorem to find x.

10. anonymous

a^2+b^2=c^2. So, 2x^2-6^2=x^2.

11. mathstudent55

Yes, you have the right idea, but you need to be careful when you write it.

12. mathstudent55

$$(2x)^2 - 6^2 = x^2$$ The parentheses are important because you will get 4x^2. Without parentheses you have 2x^2 which is incorrect.

13. mathstudent55

I'd start with $$x^2 + 6^2 = (2x)^2$$ Then change it to: $$(2x)^2 - x^2 = 6^2$$ Now continue from there.

14. mathstudent55

15. anonymous

9

16. mathstudent55

???

17. mathstudent55

The next step is $$4x^2 - x^2 = 36$$ $$3x^2 = 36$$ Divide both sides by 3 and then take the square root.

18. anonymous

oh opps i did something else

19. anonymous

x^2=12. So, x=3.4641016

20. mathstudent55

No don't find a decimal approximation. $$x^2 = 12$$ $$x = \sqrt {12}$$ $$x = \sqrt {4 \times 3}$$ $$x = 2\sqrt 3$$ Now we have x. The side of the rhombus is 2x, so multiply x by 2.

21. anonymous

Side= $4\sqrt{3}\approx6.93$

22. anonymous

I understand now. Thanks for the help @mathstudent55 :D Much appreciated.

23. mathstudent55

Excellent work! You're welcome.