The figure attached shows the dimensions of a semicircular..

[AAPL]

The figure attached shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

The OA is B.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

[GMATWisdom]

The figure attached shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

The OA is B.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

clearly the maximum width of the vehicle can be 12 feet that is 6feet on either side from the center of the road.
The diagonal of the vehicle from the center of the road should not be more than 10 feet which is the radius of the tunnel.
Now let us apply pythagorus theorem for each option while adding 1/2 feet to each option.
for option A 6^2 +6 ^2 =72 much less than 10^2 therefore bigger size vehicles can also pass. hence this is not the limit.
For option B 6^2 +8^2 = 100 which is exactly equal to 10^2. Hence this option sets the limit as no bigger size vehicles can pass through..
Hence option B is correct.

[EconomistGMATTutor]

Hello LUANDATO.

Let's take a look at this image.



The red line represents the way for the vehicles inside the tunnel. And we have a right triangle whose green cathetus represents the greatest height of the vehicles that can use the tunnel. It is $$\sqrt{10^2-6^2}=\sqrt{64}=8\ ft.$$ But, it tells us that vehicles must clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane, so the limit on the height of vehicles that are allowed to use the tunnel is $$8-\frac{1}{2}=\frac{15}{2}=7.5 ft.$$ This is why the correct answer is[spoiler] B=7½ ft[/spoiler].

I hope this explanation can help you.

Regards.