Question

(b) the lengths of the sides of a triangle are represented by three consecutive integers. if the perimeter of the triangle is 48 feet, find the lengths of its sides.

Explanation:

Step1: Define variables for sides

Let the three consecutive integers representing the side lengths be \( n \), \( n + 1 \), and \( n + 2 \).

Step2: Set up perimeter equation

The perimeter of a triangle is the sum of its side lengths. So, \( n+(n + 1)+(n + 2)=48 \).

Step3: Simplify the equation

Combine like terms: \( 3n+3 = 48 \).

Step4: Solve for n

Subtract 3 from both sides: \( 3n=48 - 3=45 \). Then divide by 3: \( n=\frac{45}{3}=15 \).

Step5: Find side lengths

First side: \( n = 15 \) feet. Second side: \( n + 1=15 + 1 = 16 \) feet. Third side: \( n + 2=15 + 2 = 17 \) feet.

Answer:

The lengths of the sides are 15 feet, 16 feet, and 17 feet.