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The lengths of the three sides of a triangle (in meters) are consecutive even 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 even integers. If the perimeter is meters, find the value of the shortest of the three side lengths.Answer: meters
- Denote Shortest Side: Let's denote the shortest side of the triangle as (in meters). Since the sides are consecutive even 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. So, we can write the equation for the perimeter as:
- Write Perimeter Equation: Now, let's simplify the equation by combining like terms:
- Simplify Equation: Next, we subtract from both sides of the equation to isolate the terms with :
- Isolate Terms with x: Now, we divide both sides of the equation by to solve for x:
- Solve for : Since represents the shortest side of the triangle, we have found that the shortest side is meters.
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