- #1
MatinSAR
- 588
- 182
- Homework Statement
- Find the sides of the right triangle so that their sum is minimized.
- Relevant Equations
- ##a^2+b^2=c^2##
Hello. We know that ##a^2+b^2=c^2## and we want to minimize ##a+b##.
$$b= \sqrt {c^2-a^2}$$ $$ \dfrac {d}{da} (a+\sqrt {c^2-a^2})=0$$ $$ 1-\dfrac {a}{ \sqrt {c^2-a^2}}=0 $$ This gives $$a=\dfrac {c}{\sqrt 2}$$
But it doesn't work for c=5. I know a=3 and b=4 minimize a+b.
$$b= \sqrt {c^2-a^2}$$ $$ \dfrac {d}{da} (a+\sqrt {c^2-a^2})=0$$ $$ 1-\dfrac {a}{ \sqrt {c^2-a^2}}=0 $$ This gives $$a=\dfrac {c}{\sqrt 2}$$
But it doesn't work for c=5. I know a=3 and b=4 minimize a+b.