Question

the perimeter of the triangle below is 34 units. find the value of y.

Explanation:

Step1: Set up perimeter equation

The perimeter of a triangle is the sum of its side - lengths. So, $3y+(y + 3)+(2y+1)=34$.

Step2: Combine like - terms

Combining the $y$ terms and the constant terms, we get $(3y+y + 2y)+(3 + 1)=34$, which simplifies to $6y+4 = 34$.

Step3: Isolate the variable term

Subtract 4 from both sides of the equation: $6y+4-4=34 - 4$, resulting in $6y=30$.

Step4: Solve for y

Divide both sides by 6: $\frac{6y}{6}=\frac{30}{6}$, so $y = 5$.

Answer:

$5$