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avatar+107 

Determine the value of ? in the figure below.

 

[asy] size(4cm);void mra(pair u, pair v, pair w, real r){ draw(v+(u-v)/length(u-v)*r--v+(u-v)/length(u-v)*r+(w-v)/length(w-v)*r--v+(w-v)/length(w-v)*r);} pair a=(-1,0); pair b=(0,0); pair c=(0,sqrt(24)); pair d=(5,sqrt(24));draw(c--a--b--c--d--b);mra(a,b,c,0.4);mra(b,c,d,0.4);label(

 Mar 31, 2019
 #1
avatar+18274 
+2

Use pythagorean theorem to find the third side of the SMALLER triangle first.....

    Then use the pythagorean theorem to find the hypotenuse of the LARGER triangle

        Let me know what you find......

 

 

 

Well...I came up with a different answer than KeyLimePi......

Smaller triangle side.....

   1^2 +s^2 = 25

    s=sqrt24

Then using the Pythag theorem on the larger triangle:   sqrt(24)^2 + 5^2 = Hyp^2

                                                                                              24 +        25 = hyp^2

                                                                                                      49= hyp^2

                                                                                                        7=? on the larger triangle

 Mar 31, 2019
edited by ElectricPavlov  Mar 31, 2019
 #2
avatar+105 
+2

Use pythagorean theorem to find the side of the smaller triangle. 

\(1^2+b^2=5^2\)

\(b=2\sqrt6\)

So continuing with the pythagorean thereom \(2\sqrt{6}^2+5^2=c^2\)

\(c=\sqrt{37}\)

I am assuming the problem asks for a square root version.

 

Yes I now realize my mistake. If you look in the beginning of my answer you see that I used \(5\) instead of  \(5^2\)

Here is my edited answer...

Use pythagorean theorem to find the side of the smaller triangle. 

\(1^2=b^2=5^2\)

\(1+b^2=25\)

\(b^2=24\)

\(b=\sqrt{24}\)

So continuing with the pythagorean thereom \(\sqrt{24}^2+5^2=c^2\)

\(24+25=c^2\)

\(24+25=49\)

\(\sqrt{49}=7\)

Therefore the answer is \(7\)

 

Thanks, ElectricPalov and SoulSlayer615 for correcting my previous error,

coolcool\(\pi\)

 Mar 31, 2019
edited by KeyLimePi  Apr 14, 2019
 #3
avatar+107 
+1

Nope it's 7 as ElectricPavlov said

SoulSlayer615  Apr 1, 2019

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