Problem 4 · 2005 AMC 8
Easy
Geometry & Measurement
perimeter-area
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?
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Answer: C — 36.
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Hint 1 of 2
'Equal perimeters' is the bridge: the triangle hands you a total length, and a square splits that same length into 4 equal sides.
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Hint 2 of 2
The decimals are a distraction. Add the three sides first — they're chosen to land on a clean whole number.
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Approach: share the perimeter, then build the square
- Triangle's perimeter: 6.1 + 8.2 + 9.7 = 24 cm. (The ugly decimals add to a tidy 24 — a hint you're on track.)
- The square has this same perimeter, so one side is 24 ÷ 4 = 6 cm.
- Area = side² = 6² = 36 sq cm.
- Sanity check: don't grab a side length and square it without dividing — 24² or 6·4 are the traps. Perimeter → side → area is the chain.
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