SOLUTION: Hello, I need here some help. I really don't get the "thing" this type of problems want me to get. I generally don't understand them. Could you help me? Here it is: "If a>0 and

Question 936639: Hello, I need here some help. I really don't get the "thing" this type of problems want me to get. I generally don't understand them. Could you help me?
Here it is: "If a>0 and b>0, compare: A. a+b B. sqrt(a^2+b^2)"
Here the possible answers are: "A" if A is greater. "B" if B is greater. "C" if both are equal, and "D" if there's not enough information to solve the problem.
Can you explain it to me?
Thank you in advance.
Found 2 solutions by rothauserc, Alan3354:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let's imagine a right triangle, ABC and sides a, b, c such that c is the hypotenuse, then we have
c^2 = a^2 + b^2
as an example chose a 3, 4, 5 right triangle with c = 5, then
3^2 + 4^2 = 25 and 3 + 4 = 7 and
a^2+b^2 = 25 and square root(25) = 5 < 3+4 = 7
the answer is A

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
"If a>0 and b>0, compare: A. a+b B. sqrt(a^2+b^2)"
Here the possible answers are: "A" if A is greater. "B" if B is greater. "C" if both are equal, and "D" if there's not enough information to solve the problem.
Can you explain it to me?
==============================
Square both the values A & B
A. (a+b)^2 = a^2 + 2ab + b^2
B. (sqrt(a^2+b^2))^2 = a^2 + b^2
-----
A^2 is greater by 2ab --> a+b is greater (by how much is not known)
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