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Cost of a triangular plot with sides 55, 62, 117

Question

A seller offers you a triangular plot whose sides measure 5555, 6262 and 117117 yards, priced at $10 per square yard. How much does the plot cost?

Short answer

$0. Since 55+62=11755+62=117, the triangle inequality fails with equality: the three sides lie on one straight line and enclose no area, so there is nothing to pay for.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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