Question

question
the lengths of the three sides of a triangle (in feet) are consecutive integers. if the perimeter is
90 feet, find the value of the longest of the three side lengths.
answer
feet
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consecutive integer problems - linear (level 1)

Explanation:

Step1: Define the sides

Let the three consecutive integers be \(x\), \(x + 1\), \(x+2\) (where \(x+2\) is the longest side).

Step2: Set up the perimeter equation

The perimeter \(P=x+(x + 1)+(x+2)\). Given \(P = 90\), so \(x+(x + 1)+(x+2)=90\).
Simplify the left - hand side: \(3x+3 = 90\).

Step3: Solve for \(x\)

Subtract 3 from both sides: \(3x=90 - 3=87\).
Divide both sides by 3: \(x=\frac{87}{3}=29\).

Step4: Find the longest side

The longest side is \(x + 2\). Substitute \(x = 29\) into \(x + 2\), we get \(29+2=31\).

Answer:

31