Question

Find the length of a side of rhombus ABCD if AE=6".

Answer 1

What do you know about the diagonals of a rhombus?

Answer 2

AD=12"

Answer 3

CB=2x

Answer 4

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

Answer 5

What is the other property?

Answer 6

The are perpendicular to each other.

Answer 7

Also, all sides of a rhombus are congruent.

Answer 8

Now you can use the Pythagorean theorem to find x.

Answer 9

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

Answer 10

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

Answer 11

\((2x)^2 - 6^2 = x^2\)

The parentheses are important because you will get 4x^2. Without parentheses you have 2x^2 which is incorrect.

Answer 12

I'd start with

\(x^2 + 6^2 = (2x)^2\)

Then change it to:

\((2x)^2 - x^2 = 6^2\)

Now continue from there.

Answer 13

Did you get an answer?

Answer 14

9

Answer 15

???

Answer 16

The next step is

\(4x^2 - x^2 = 36\)

\(3x^2 = 36\)

Divide both sides by 3 and then take the square root.

Answer 17

oh opps i did something else

Answer 18

x^2=12. So, x=3.4641016

Answer 19

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.

Answer 20

Side= \[4\sqrt{3}\approx6.93\]

Answer 21

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

Answer 22

Excellent work!
You're welcome.