Can someone help me solve #1 and #9 in the picture, I'm having trouble on getting started with these problems and understanding the quadratic formula.

*UPDATE: I attached the file of the image scan to this thread can you see it now?*

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- Jul 12th 2012, 09:52 AMMocotauganFind the value of the variables
Can someone help me solve #1 and #9 in the picture, I'm having trouble on getting started with these problems and understanding the quadratic formula.

*UPDATE: I attached the file of the image scan to this thread can you see it now?* - Jul 12th 2012, 10:32 AMbritmathRe: Find the value of the variables
The attached image isn't displaying, can you try again, or just type the relevant questions?

- Jul 12th 2012, 12:10 PMReckonerRe: Find the value of the variables
For 1-8, you should know that the altitude of a right triangle (with the hypotenuse as the base) divides the triangle into two smaller triangles that are each similar to the larger triangle (and to each other). So the corresponding sides of each triangle will be in the same proportion. Therefore, in problem 1 for example,

$\displaystyle \frac y{10} = \frac2y\Rightarrow y^2 = 20\Rightarrow y=2\sqrt5.$

Use a similar procedure to find $\displaystyle x$:

$\displaystyle \frac x8 = \frac2x\Rightarrow x^2 = 16\Rightarrow x=4.$

For 9 and 10, know that the median of a right triangle (on its hypotenuse) divides the triangle into two smaller isosceles triangles (the length of this median is half the length of the hypotenuse).