3 Geometry-Algebra Problems Need Help Please

G

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Hey all I am in 9th grade taking Geometry 9A Honors. I have been sick the last couple of days and in need of help of these three problems that i have tried countless times:

25.

This problem I just can't seem to do. I've tried and tried this problem for countless minutes.

number_25.gif


27.

number_27.gif


I have tried this problem and I am stuck and don't know what to do next:

number_27_tryout.gif


number_27_tryout2.gif


28.

This problem is making my brain go haywaire the most:

number_28.gif


I tried but am stuck:

number_28_tryout.gif




Thanks guys and I hope you can help me on this.
 
For #25, let the length of EF be x. Then FG will be 21-x.

Equate using Pyhtagoras:

\(\displaystyle \sqrt{17^{2}-x^{2}}=\sqrt{10^2-(21-x)^{2}}\)

See?. Now, solve for x. You should be able to use this to easily find HF.
 
Ok thanks galactus. I think I've got it.

Any help on the other problems would greatly be appreciated.

Thnaks!
 
Hello, AirForceOne!

You were on the right track with #28 . . .

You had: \(\displaystyle \,a^2\,+\,b^2\:=\:c^2\)

Your next statements should have been: \(\displaystyle \,\begin{array}{cc}x^2\,+\,(2y)^2\:=\:73 \\ (2x)^2\,+\,y^2\;=\;52\end{array}\)

Then solve the system: \(\displaystyle \:\begin{array}{cc}x^2\,+\,4y^2\:=\:73 \\ 4x^2\,+\,y^2\:=\:53\end{array}\)

I'll assume you know how to do that . . .
 
Hello, AirForceOne!

There's something very strange about #27 . . .
\(\displaystyle \;\;\)Look at it again.
Code: 
             *P
            /|
           / |
        25/  |
         /   |20
        /    |
       /     |
      * - - -*
      K   ?   M
Whether the ladder was moved or not: \(\displaystyle KM\,=\,15\)
 
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