A triangle's sides are in a ½: 1/3: ¼ ratio with a 52 cm perimeter. Find the shortest side________?
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Answer: D. 12cm
Explanation
Simplifying the fractional ratio of one half to one third to one quarter yields six to four to three. Multiplying each ratio part by a common variable x gives side lengths of six x and four x and three x. Summing these algebraic side lengths to equal the perimeter of fifty two centimeters solves for x as four. The perimeter of any geometric triangle is calculated by finding the total sum of all three outer side lengths. Fractions in ratios are converted to whole numbers by multiplying every term by the least common multiple of denominators. Algebraic equations allow unknown side lengths to be determined efficiently once the scale factor is accurately computed.
Nine centimeters is incorrect because it fails to match the derived scale factor of four for the shortest side. Ten centimeters results from an improper distribution of the perimeter value among the fractional ratio components. Eleven centimeters is mathematically inconsistent with the solved algebraic value derived from the perimeter equation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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