If you know that AC=3,AB=4,XY=1,then what is XW=?

WXYZ and ABCD are rectangulars

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- Jun 8th 2012, 03:28 PMMhmh96Finding the length of line
If you know that AC=3,AB=4,XY=1,then what is XW=?

WXYZ and ABCD are rectangulars

http://store3.up-00.com/June12/zd594451.jpg - Jun 8th 2012, 10:39 PMSorobanRe: Finding the length of line
Hello, Mhmh96!

Quote:

Draw diagonal

Triangle is a 3-4-5 right triangle.

We find that and are parallel to

And**all**the right triangles are similar.

Can you finish the problem?

- Jun 8th 2012, 10:45 PMMhmh96Re: Finding the length of line
Actually no Soroban,can you explain more .

- Jun 8th 2012, 10:50 PMProve ItRe: Finding the length of line
- Jun 8th 2012, 11:08 PMProve ItRe: Finding the length of line
I'm going to call length , length and .

From the smallest triangles, we can see that by Pythagoras.

We can also see from the larger triangles that

Now note that the area of the largest rectangle is . If we evaluate the area of each smaller piece, we find

Substituting , (since we know ) will enable solving for , which will enable solving for , and finally solving for .

See how you go. - Jun 10th 2012, 04:40 AMbjhopperRe: Finding the length of line
Following Soroban's hint I calculated

WX= 4.25= ( 17/5) / cos 36.87

ZY = 3.66 = (11/5 /sin 36.87

WXYZ is not a rectangle but a trapezoid - Jun 10th 2012, 06:42 AMBobPRe: Finding the length of line
The rectangle has to be in a particular position, the angle AXW being approximately 31.7501 degrees.

WX turns out to be approximately 4.08512.