GmatGreen wrote:
In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?
A) 10 - 5root(3)
B) 10 - 5root(2)
C) 2
D) 2.5
4) 4
Solution:
We are being asked to determine the length of RS. To determine this length we need to know the length from point R to the right angle in the given figure. If we label the point at the right angle as T, we see that we need to determine the length of TR.
If we draw a line segment connecting V and R, we will see that VR, VT and TR create a right triangle. Furthermore, we are told in the question stem that VR (the hypotenuse) is 10, and that one of the sides, VT, is 5, so we now plug these values into the Pythagorean Theorem.
TR^2 + VT^2 = VR^2
TR ^2 + 5^2 = 10^2
TR ^2 + 25 = 100
TR ^2 = 75
TR = √75
TR = √25 x √3
TR = 5√3
So TR is 5√3. We subtract this from the total length TS, which is 10, to determine the length from R to S:
10 - 5√3
Answer:
A
