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Find the Fourth Side

```
Date: 12/03/2001 at 20:48:36
From: Suzy

The successive sides of a quadrilateral are 2,6,9, and x. If the
diagonals of the quadrilateral are perpendicular, compute x.
```

```
Date: 12/04/2001 at 08:17:15
From: Doctor Floor

Hi, Suzy,

The diagonals of the quadrilateral divide the figure into four right
triangles:

From the three right triangles with known hypotenuses we see that:

t^2 + u^2 = 4    [1]
u^2 + v^2 = 36   [2]
v^2 + w^2 = 81   [3]

Now, if we compute [1]-[2]+[3] we get:

t^2 + u^2 - u^2 - v^2 + v^2 + w^2 = 4 - 36 + 81
t^2 + w^2 = 49

And thus we see that x must be equal to 7.

If you have more questions, just write back.

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons

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