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Question
The hypotenuse of a right-angled triangle has the length 10 cm. Find the
maximum perimeter. I'm thinking you have to use the pythagoream theorm but
I'm not sure how to incorporate it into the problem.
Perimeter of right-angled triangle is P=a+b+c where c=√(aČ+bČ).
So we know that 10=√(aČ+bČ), that menas 100=aČ+bČ, this gives us :
a=√(100-bČ). Now we, derive P with respect to b :
P(b)=√(100-bČ)+b+10
P'(b)=-b/√(100-bČ) + 1
To find maximum , we solve P'(b)=0 :
-b/√(100-bČ) + 1 = 0
b/√(100-bČ)=1
b=√(100-bČ)
bČ=100-bČ
2bČ=100
bČ=50
b=7.07
Therefore , P(7.07)=√(100-50)+7.07+10 = 24.14
Alon.
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Answers by Expert:
Alon Mandes
Expertise
Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
Experience
1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.
Education/Credentials
M.A in Mathematics & Bs.c in Electronics.
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