Question

Karl wants to find the width RQ of a river. He starts at point R, and walks perpendicular along the edge of the river 42 ft and marks point S. He then walks 28 ft further and marks point T. He turns 90° and walks until his location (point U), point S, and point Q are collinear. Suppose TU = 68 ft. What is the width of the river in feet?

Answer 1

• 102 ft

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According to the question, triangles SQR and SUT are similar as per AA similarity (one right angle and one pair of vertical angles).

We know that corresponding sides of similar triangles have same ratio.

Set up equal ratios and find the missing side RQ:

• RQ/UT = SR/ST
• RQ/68 = 42/28
• RQ/68 = 3/2
• RQ = 68*3/2
• RQ = 102

The width of the river is 102 feet.