2019/20 AHSMC Part 1 Problem 10

Problem 10 of 16

A tall cabinet $52$ cm wide is standing $50$ cm away from a table $120$ cm high. The cabinet is tilted until it touches the top of the table, as in the figure.

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How far from the floor (in cm) is the corner $C$ of the cabinet? Note that the figure is not drawn to scale.

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Solution

In the figure, the length of the hypotenuse of the right triangle with side lengths $50$ and $120$ is $\sqrt{2500 + 14400} = 130$ . The two right triangles are similar hence, if $x$ denotes the distance in cm of point $C$ from the floor, $\frac{50}{130} = \frac{x}{52} \iff x = 20.$ The answer is (C).

University of Alberta

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