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The lengths of the three sides of a triangle (in inches) are consecutive integers. If the perimeter is inches, find the value of the middle of the three side lengths.Answer: inches
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Q. The lengths of the three sides of a triangle (in inches) are consecutive integers. If the perimeter is inches, find the value of the middle of the three side lengths.Answer: inches
- Denote Triangle Side Lengths: Let's denote the lengths of the three sides of the triangle as , , and , where is the length of the middle side. Since the sides are consecutive integers, this is a reasonable assumption.
- Perimeter Equation: The perimeter of the triangle is the sum of the lengths of its sides. So, we can write the equation for the perimeter as: + x + =
- Simplify Equation: Simplify the equation by combining like terms:
- Solve for x: Divide both sides of the equation by to solve for x:
- Check Other Sides: Now that we have the value of , which is the length of the middle side, we can check if the other two sides are indeed consecutive integers:The smaller side is .The larger side is .
- Verify Sum: We can verify that the sum of these three sides equals the perimeter:
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