How Do You Solve the Rhombus Side Length in Rectangle ABCD?

[ThienNguyen]

Homework Statement

In Rectangle ABCD, AB=4 and BC=3. Find the side length of Rhombus AXYZ, where X is on AB, Y is on BC and Z is on BD.

2. Relevant Questions:

The Attempt at a Solution

Hi, so here's my picture for the problem...I tried to draw the exact picture with exact value of the problem (using rulers, compass, etc.)
https://mail.google.com/mail/u/0/?ui=2&ik=65096f80a0&view=fimg&th=142e05c217ab4a7e&attid=0.1&disp=inline&safe=1&attbid=ANGjdJ8VlUlSyOcZxwQH7UU8SWsWZZS5AQMIGuuyqaGtZEzxSajqjBH3pw_2NeEwrZCyqh-ea_Lq9g6IEgwbZ80bNLtI2nwqrzmgJlmwZALZiJEnTpNHIJZJno8zncw&ats=1386743610684&rm=142e05c217ab4a7e&zw&sz=w1488-h627
I was able to find a pair of similar triangles and figured out that: YZ = (4/3)BY
I didn't get really far after that...
Please help me !

 

[ehild]

Homework Statement

In Rectangle ABCD, AB=4 and BC=3. Find the side length of Rhombus AXYZ, where X is on AB, Y is on BC and Z is on BD.

2. Relevant Questions:

The Attempt at a Solution

Hi, so here's my picture for the problem...I tried to draw the exact picture with exact value of the problem (using rulers, compass, etc.)
https://mail.google.com/mail/u/0/?ui=2&ik=65096f80a0&view=fimg&th=142e05c217ab4a7e&attid=0.1&disp=inline&safe=1&attbid=ANGjdJ8VlUlSyOcZxwQH7UU8SWsWZZS5AQMIGuuyqaGtZEzxSajqjBH3pw_2NeEwrZCyqh-ea_Lq9g6IEgwbZ80bNLtI2nwqrzmgJlmwZALZiJEnTpNHIJZJno8zncw&ats=1386743610684&rm=142e05c217ab4a7e&zw&sz=w1488-h627
I was able to find a pair of similar triangles and figured out that: YZ = (4/3)BY
I didn't get really far after that...
Please help me !

YZ = (4/3)BY is correct. Use the other property of the rhombus, that all sides are of equal length.ehild

 

[ET ag]

is a rhombus implies

. In

by similarity we get

And then we get

. Thus, we result in the equation

.

Sorry if the LaTeX or images I put in my reply don't come out properly

ET ag