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Geometry

by swerve » Mon Feb 03, 2020 3:54 pm
squirrelonwire_figure.PNG
A squirrel climbs a straight wire from point A to point C. If B is the midpoint of AC, how far above the ground is point B?

1) Point C is 40 feet above the ground.
2) \(x=60\)

The OA is A

Source: Magoosh
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Source: — Data Sufficiency |

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Re: Geometry

by Jay@ManhattanReview » Mon Feb 03, 2020 10:27 pm
swerve wrote: ↑
Mon Feb 03, 2020 3:54 pm
 squirrelonwire_figure.PNG

A squirrel climbs a straight wire from point A to point C. If B is the midpoint of AC, how far above the ground is point B?

1) Point C is 40 feet above the ground.
2) \(x=60\)

The OA is A

Source: Magoosh
Drop a perpendicular from point B on the ground; say that point is B' and say that BB' = y feet. We have to get the value of y.

Let's take each statement one by one.

1) Point C is 40 feet above the ground.

Again, drop a perpendicular from point C on the ground; say that point is C'; thus, CC' = 40 feet.

Say AC = 2x, thus, AB = 2x/2 = x

Thus, ∆ABB' and ∆ACC' are similar triangles.

=> 40/y = 2x/x => y 20. Sufficient.

2) \(x=60\)

Certainly insufficient.

The correct answer: A

Hope this helps!

-Jay
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