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?

Firewolf Aug 10, 2019

#1**+1 **

*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 a^{2} + b^{2} + c^{2} = 1800

by the Pythagorean theorem a^{2} + b^{2} = c^{2}

substitute c^{2} for a^{2} + b^{2} in original c^{2} + c^{2} = 1800

combine terms 2c^{2} = 1800

divide both sides by 2 c^{2} = 900

take square root of both sides c = sqrt 900 = __+__30

discard the negative root c = 30

.

Guest Aug 10, 2019

edited by
Guest
Aug 10, 2019

#2**0 **

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

Guest Aug 11, 2019

#3**0 **

\(a^2+b^2=c^2\\ a^2+b^2+c^2=1800\\ so\\ 2c^2=1800\\ c^2=900\\ c=30units \)

The hypotenuse is 30 units long.

Melody Aug 11, 2019

#4**+1 **

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.

.

Guest Aug 11, 2019

#5**+2 **

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

#6**0 **

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