Question

a triangle has dimensions represented by the expressions shown. which expression represents the perimeter of the triangle? 9y + 3 9y + 7 6y - 2 5y + 5

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So we add \(2y\), \(4y - 2\), and \(3y + 5\).

$$ \text{Perimeter} = 2y+(4y - 2)+(3y + 5) $$

Step2: Combine like terms

First, combine the \(y\)-terms: \(2y + 4y+3y=9y\). Then combine the constant terms: \(-2 + 5 = 3\).

$$ \text{Perimeter}=9y + 3 $$

Wait, that seems conflicting. Wait, let's re - calculate the constant terms: \(-2+5 = 3\)? Wait, no: \(2y+(4y - 2)+(3y + 5)=2y + 4y+3y-2 + 5=(2y + 4y+3y)+(-2 + 5)=9y+3\)? But wait, maybe I made a mistake. Wait, \(4y-2+2y + 3y + 5=(4y+2y+3y)+(-2 + 5)=9y + 3\). But let's check again. Wait, the three sides are \(2y\), \(4y - 2\), \(3y+5\). So adding them: \(2y+4y - 2+3y + 5=(2y + 4y+3y)+(-2 + 5)=9y + 3\). But wait, the options have \(9y + 3\) as one of the options. Wait, but maybe I miscalculated the constant terms. Wait, \(-2+5 = 3\), yes. So the perimeter is \(9y + 3\).

Answer:

\(9y + 3\) (the option with this expression)