Question

design an art class is making a mural for their school which has a triangle drawn in the middle. the length of the bottom of the triangle is (y + 4). another side is 3 less than 2 times the length of the bottom of the triangle. the last side is 2 more than the bottom of the triangle. write and simplify an expression for the perimeter of the triangle. what is the expression for the perimeter of the triangle? (simplify your answer.)

Explanation:

Step1: Define bottom side length

Let the bottom side length be $s_1 = y + 4$.

Step2: Find second side length

Calculate the second side: $s_2 = 2(y + 4) - 3 = 2y + 8 - 3 = 2y + 5$.

Step3: Find third side length

Calculate the third side: $s_3 = (y + 4) + 2 = y + 6$.

Step4: Sum sides for perimeter

Perimeter $P = s_1 + s_2 + s_3$
$P = (y + 4) + (2y + 5) + (y + 6)$

Step5: Simplify the expression

Combine like terms: $P = (y + 2y + y) + (4 + 5 + 6) = 4y + 15$

Answer:

$4y + 15$