Question

question: if a triangle has sides of lengths x, x - 2, and x + 4 and a perimeter of 23, what is the length of the shortest side of the triangle? a. 2 b. 5 c. 7 d. 12

Explanation:

Step1: Set up perimeter equation

The perimeter of a triangle is the sum of its side - lengths. So, $x+(x - 2)+(x + 4)=23$.

Step2: Simplify the left - hand side

Combine like terms: $(x+x+x)+(-2 + 4)=3x+2$. So, $3x+2 = 23$.

Step3: Solve for x

Subtract 2 from both sides: $3x=23 - 2=21$. Then divide both sides by 3: $x=\frac{21}{3}=7$.

Step4: Find the side - lengths

The side - lengths are: $x = 7$, $x-2=7 - 2 = 5$, $x + 4=7+4 = 11$.

Answer:

11