$17 \cdot 154$ Let $P_{1}, P_{2}, P_{3}$ be the equilateral triangles constructed on the sides $AB$, $BC$, $CA$ of the right triangle $\triangle ABC$ (with $C$ as the right angle). Then the $(\quad)$ of $P_{1}$ is the sum of the ( ) of $P_{2}$ and $P_{3}$.
(A) area, area.
(B) perimeter, perimeter.
(C) sum of interior angles, sum of interior angles.
(D) altitude on side $AB$, altitudes on sides $BC$ and $CA$.
(2nd "Five Sheep Cup" Junior High School Mathematics Competition, 1990)
［Solution］By the Pythagorean theorem and the given conditions, we know
$$
A B^{2}=A C^{2}+B C^{2} \text {. }
$$

Also, $\quad S_{p_{1}}=\frac{\sqrt{3}}{4} A B^{2}, S_{p_{2}}=\frac{\sqrt{3}}{4} B C^{2}$,
$$
S_{p_{3}}=\frac{\sqrt{3}}{4} A C^{2} \text {. }
$$

Therefore,
$$
S_{p_{1}}=S_{p_{2}}+S_{p_{3}} .
$$

Hence, the correct choice is $(A)$.