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The lengths of the four sides of a quadrilateral (in centimeters) are consecutive integers. If the perimeter is centimeters, find the value of the longest of the four side lengths.Answer: centimeters
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Q. The lengths of the four sides of a quadrilateral (in centimeters) are consecutive integers. If the perimeter is centimeters, find the value of the longest of the four side lengths.Answer: centimeters
- Denote smallest side as : Let's denote the smallest side of the quadrilateral as (in centimeters). Since the sides are consecutive integers, the other three sides will be , , and centimeters long. The perimeter of the quadrilateral is the sum of the lengths of its sides, which is given as centimeters. So, we can write the equation for the perimeter as:
- Write perimeter equation: Now, let's simplify the equation by combining like terms:
- Simplify the equation: Next, we subtract from both sides of the equation to solve for :
- Solve for n: Now, we divide both sides of the equation by to find the value of :
- Calculate longest side: Since is the smallest side, the longest side will be . So, we calculate the length of the longest side:Longest side = Longest side = Longest side = centimeters
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