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Two vertical posts of heights 6 m and 12 m stand 30 m apart on level…
Question
Two vertical posts of heights 6 m and 12 m stand 30 m apart on level ground. A single wire runs from the top of the first post down to a point P on the ground between them, then up to the top of the second post. Let L be the minimum possible total length of wire. Find L^2.
✓ Verified answer: 1224checked by our engine — not a guess
Step-by-step solution
Place the bases at x = 0 and x = 30; let P be at distance x from the first base.
The wire length is L(x) = sqrt(x^2 + 6^2) + sqrt((30-x)^2 + 12^2).
By the reflection principle, reflect the top of the first post (0, 6) to (0, -6); the minimum total path equals the straight-line distance from (0, -6) to (30, 12): sqrt(30^2 + (12+6)^2) = sqrt(900 + 324) = sqrt(1224).
Hence L^2 = 1224.
Final answer1224
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