+239 In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?
In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?
call the legs a and b and call the hypotenuse c
given a2 + b2 + c2 = 1800
by the Pythagorean theorem a2 + b2 = c2
substitute c2 for a2 + b2 in original c2 + c2 = 1800
combine terms 2c2 = 1800
divide both sides by 2 c2 = 900
take square root of both sides c = sqrt 900 = +30
discard the negative root c = 30
.
This is simply 3 - 4 - 5 triangle scaled up by a factor of 6 as follows:
[3 x 6 ]^2 + [4 x 6]^2 =[ 5 x 6]^2
18^2 + 24^2 = 30^2
900 = 900
For a total = 1,800
+118673 \(a^2+b^2=c^2\\ a^2+b^2+c^2=1800\\ so\\ 2c^2=1800\\ c^2=900\\ c=30units \)
The hypotenuse is 30 units long.
Meloody, why did you post this answer which is exactly like the answer I posted yesterday? I'm not being accusatory or anything like that; I genuinely want to know why. Thanks.
.
+2489 Probably to check and confirm your work.
Guests are notorious for posting wrong answers, errant logic, and just plain blarney and bullshit.
There a few longtime guests who perpetually do this very thing. I call them the BBs. I can usually recognize them because they all write with quills. One of them often commands his computer to write with a quill –it never seems to run out of ink. 
GA
+118673 Yea sorry
There were 2 answers and they were different.
It often takes less effort to answer a question then it does to check the answers that are already there.
I do appologize though, your answer was a very good one and it was rude of me to not acknowledge it.
To be honest I did not even look at your answer, other than to recognise that 30 corresponded to my answer.
I did give you a point in acknowledgment but I do not consider that that was enough.
All I can do is offer you my appology.
Why don't you join up and then you will get a reputation for being a reliable, good quality, answerer. 
