What is the length of MN?

Consider the following for the next two (02) items that follow:<br>Let two parallel line segments PQ=5 cm and RS=3 cm be perpendicular to a horizontal line AB, as shown in the figure given below. The point of intersection of PS and QR is M and MN is perpendicular to QS.

  1. A. \frac{3}{8} cm
  2. B. \frac{5}{8} cm
  3. C. \frac{9}{8} cm
  4. D. \frac{15}{8} cm

Correct Answer: D. \frac{15}{8} cm

Explanation

This is a standard crossed-ladders property where the height h of the intersection point of diagonals drawn from the bases of two parallel vertical poles of heights a and b is h = \frac{ab}{a+b}. Given a=5 and b=3, MN = \frac{5 \times 3}{5 + 3} = \frac{15}{8} cm.

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