Right angled triangle

[mathmath]

In a right-angled triangle, the sum of the squares of the three sides is 18. The length of the hypotenuse is...

(A) √18 (B) 3 (C) 9 (D)4 (E) 9/2


With the answer, please show the solution! Thankyou so so much! :smile:

 

[Ishuda]

What formula does the problem produce? From the Pythagorean Theorem, what is the relationship between the sides of the right triangle and the hypotenuse?

 

[pka]

In a right-angled triangle, the sum of the squares of the three sides is 18. The length of the hypotenuse is...
With the answer, please show the solution!

First question: What gives you the right to demand that we show you a solution?

In a right-angled triangle, the sum of the squares of the three sides is 18. The length of the hypotenuse is...(A) √18 (B) 3 (C) 9 (D)4 (E) 9/2

Now that the two mathematical geniuses have had at each other, I can give a mathematician's advice.
Suppose that each of \(\displaystyle x,~y,~\&~z\) is the length of a side of that triangle.
Then if \(\displaystyle z\) is the length of its hypotenuse we have \(\displaystyle x^2+y^2+z^2=18~\&~x^2+y^2=z^2\).

So \(\displaystyle \large 2z^2=18\).