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The lengths of the three sides of a triangle (in meters) are consecutive integers. If the perimeter is meters, find the value of the longest of the three side lengths.Answer: meters
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Q. The lengths of the three sides of a triangle (in meters) are consecutive integers. If the perimeter is meters, find the value of the longest of the three side lengths.Answer: meters
- Denote shortest side: Let's denote the shortest side of the triangle as meters. Since the sides are consecutive integers, the other two sides will be meters and meters. The perimeter of the triangle is the sum of the lengths of its sides, which is given as meters. We can set up the following equation to represent this relationship:
- Set up equation: Now, we simplify the equation by combining like terms:
- Simplify equation: Next, we subtract from both sides of the equation to isolate the term with :
- Isolate term with n: Now, we divide both sides of the equation by to solve for n:
- Solve for : Since represents the shortest side, the longest side will be . We already found that , so the longest side is: meters
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