In a right-angled triangle, the sum of the squares of the three side lengths is 1800 . The length of its hypotenuse is
(A) $\sqrt{1800}$
(B) $\frac{1}{2} \sqrt{1800}$
(C) 90
(D) 30
(E) 45
Suppose the side lengths of the triangle are $a, b$, and $c$, with $c$ the hypotenuse.

Then $c^{2}=a^{2}+b^{2}$ by the Pythagorean Theorem.

We are told that $a^{2}+b^{2}+c^{2}=1800$.

Since $a^{2}+b^{2}=c^{2}$, then $c^{2}+c^{2}=1800$ or $2 c^{2}=1800$ or $c^{2}=900$ or $c=30$ (since the side lengths are positive).

So the hypotenuse has length 30 .

ANSwER: (D)