1. In a right-angled triangle, the square of the hypotenuse is exactly equal to twice the product of the two legs. Then, the ratio of the three sides of this triangle is ( ).
(A) $3: 4: 5$
(B) $1: 1: 1$
(C) $2: 3: 4$
(D) $1: 1: \sqrt{2}$
$-1 . \mathrm{D}$
Let the two legs be $a$ and $b$. Then $a^{2}+b^{2}=2 a b \Rightarrow a=b$. Therefore, the ratio of the three sides of this right triangle is $1: 1: \sqrt{2}$.