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# 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?

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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?

Aug 10, 2019

#1
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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

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Aug 10, 2019
edited by Guest  Aug 10, 2019
#2
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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

Aug 11, 2019
#3
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\(a^2+b^2=c^2\\ a^2+b^2+c^2=1800\\ so\\ 2c^2=1800\\ c^2=900\\ c=30units \)

The hypotenuse is 30 units long.

Aug 11, 2019
#4
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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.

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Guest Aug 11, 2019
#5
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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

GingerAle  Aug 11, 2019
edited by GingerAle  Aug 11, 2019
#6
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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. Melody  Aug 11, 2019