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The lengths of the three sides of a triangle (in meters) are consecutive odd integers. If the perimeter is meters, find the value of the shortest 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 odd integers. If the perimeter is meters, find the value of the shortest of the three side lengths.Answer: meters
- Denote shortest side as : Let's denote the shortest side of the triangle as (in meters). Since the sides are consecutive odd integers, the other two sides will be and respectively. The perimeter of the triangle is the sum of its side lengths, which is given as meters. We can set up the following equation to represent this relationship:
- Simplify the equation: Now, let's simplify the equation by combining like terms:
- Subtract to isolate : Next, we subtract from both sides of the equation to isolate the terms with :
- Divide to solve for x: Now, we divide both sides of the equation by to solve for :
- Check side lengths: Since represents the shortest side of the triangle, we have found that the shortest side is meters long. We should check to make sure that the other two sides are indeed odd integers and that their sum equals the perimeter: (shortest side) + (second side) + (third side) =
- Check side lengths: Since represents the shortest side of the triangle, we have found that the shortest side is meters long. We should check to make sure that the other two sides are indeed odd integers and that their sum equals the perimeter: (shortest side) + (second side) + (third side) = Adding the side lengths to check if they sum up to the perimeter:This confirms that the side lengths are consecutive odd integers and their sum is equal to the given perimeter.
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