Rectangle $A B C D$ has side length $A B=16 \mathrm{~m}$ and diagonal length $A C=34 \mathrm{~m}$, as shown. The perimeter of rectangle $A B C D$ is
(A) $46 \mathrm{~m}$
(B) $126 \mathrm{~m}$
(C) $100 \mathrm{~m}$
(D) $92 \mathrm{~m}$
(E) $240 \mathrm{~m}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-016.jpg?height=206&width=422&top_left_y=1182&top_left_x=1296)
In $\triangle A B C, \angle A B C=90^{\circ}$ and so by the Pythagorean Theorem, $B C^{2}=34^{2}-16^{2}=1156-256$ or $B C^{2}=900$ and so $B C=\sqrt{900}=30 \mathrm{~m}$.

The perimeter of $A B C D$ is $16+30+16+30=92 \mathrm{~m}$.

ANSWER: (D)