Carcass wrote:
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A photographer is using a bipod to steady his camera while taking pictures, as shown in the figure above. The legs of the bipod are 5 feet long and are currently 6 feet apart. If he pulls the legs another 2 feet apart (1 foot on each side), the top of the bipod drops x feet.
Quantity A |
Quantity B |
1 |
x |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
KUDOS for the right solution and explanation
[b]Remind the following steps to solve a Geometry question.
1. Write down all conditions given in a question.
2. If we don't have any clue at step 1, we should try to find out any proper adjoint lines.[\b]
In this question, the heights are their adjoint lines.
The triangle with the base \(5\) is the height \(4\) and the triangle with the base \(4\) has the height \(\sqrt{21}\) from Pythagorean Theorem, since we have \(5^2 = 2^2 + \sqrt{21}^2\) and \(5^2 = 3^3 + 4^2\).
Then we have \(x = \sqrt{21} - 4\).
Since we have \(4 = \sqrt{16} < \sqrt{21} < \sqrt{25} = 5\), we have \(0 < x = \sqrt{4} < 5 - 4 = 1\) or \(x < 1\).
Therefore, A is the right answer.
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