Question

Convex hexagon ABCDEF has exactly two distinct side lengths. Side AB measures 5 units, and side BC measures 6 units. The perimeter of hexagon ABCDEF is 34 units. How many sides of hexagon ABCDEF have measure 6 units?

Answer 1

4

Explanation:

If all sides measured $6$ units, the total perimeter would be $36$. But this is $2$ too many units, so we must change two of these sides to $5$ units. Thus $\boxed{4}$ sides measure $6$ units.

Answer 2

4

Explanation:

If all were measure 5, the perimeter would be 30. The perimeter is 4 more than that. Each side that is 6 instead of 5 adds 1 to the perimeter, so there are 4 sides of length 6.

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Check

2×5 + 4×6 = 10 + 24 = 34 . . . . the answer checks OK