Two vertical towers, $A B$ and $C D$, are located $16 \mathrm{~m}$ apart on flat ground, as shown. Tower $A B$ is $18 \mathrm{~m}$ tall and tower $C D$ is $30 \mathrm{~m}$ tall. Ropes are tied from $A$ to $C$ and from $B$ to $C$. Assuming the ropes are taut, the total length of rope, in $\mathrm{m}$, is
(A) 54
(D) 48
(B) 64
(C) 44
(E) 59

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-117.jpg?height=686&width=553&top_left_y=111&top_left_x=1329)
By the Pythagorean Theorem, the length of the rope joining $B$ to $C$ is

$\sqrt{16^{2}+30^{2}}=\sqrt{256+900}=\sqrt{1156}=34 \mathrm{~m}$.

We must also determine the length of rope joining $A$ to $C$. To get from $A$ to $C$ we must go over $16 \mathrm{~m}$ and up $12 \mathrm{~m}$ (the difference between the heights of the towers), so the rope has

length $\sqrt{16^{2}+12^{2}}=\sqrt{256+144}=\sqrt{400}=20 \mathrm{~m}$.

Therefore, the total length of rope used is $54 \mathrm{~m}$.

Answer: (A)