## perl 4 years ago Maggie has a kite with the dimensions shown below. What is the width of the kite?

1. perl
2. perl

im not sure what theorem is used here

3. perl

whats up rooma

4. perl

rumoor

5. Directrix

|dw:1328862799911:dw|To find x, this theorem is used. If an altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the lengths of the segments of the hypotenuse.

6. Directrix

11 is to x as x is to 25. 11/x = x/25 x^2 = 25*11 x = 5 √ 11

7. Directrix

The width of the kite is 2 times ( 5 √ 11 = 10 √ 11

8. perl

woops, didnt see that right angle there, yes makes sense now

9. anonymous

You don't need that theorem just use pyhtagoras theorem on the three triangles. If the remainng side lenghts are y and z. x^2+25^2=y^2 and x^2+11^2=z^2. and y^2+z^2=36^2. 2x^2+25^2+11^2=36^2.

10. perl

where are you getting y^2 + z^2 = 36^2

11. perl

oh i see, yes you can prove it that way

12. perl

so you actually proved the general result |dw:1328881279082:dw|

13. perl

and after doing some algebra we have h = sqrt (ab)

14. perl

so this geometric mean theorem falls out from pythagorean theorem

Or properties of similar triangles (proportions) a:h :: h:b 11:h :: h:25 $h ^{2}=11 X 25$$h = \sqrt{11X25}=5\sqrt{11}$