Question

1. rob would like to create a triangle that is seven less than twice the perimeter of the triangle below. give an expression for the perimeter of the new triangle in simplest form.

Explanation:

Step1: Calculate the perimeter of the given triangle

The perimeter $P$ of a triangle is the sum of its side - lengths. So, $P=(y + 9)+2y+(4y-1)$. Combine like - terms: $P=(y + 2y+4y)+(9 - 1)=7y + 8$.

Step2: Find the perimeter of the new triangle

The perimeter of the new triangle is seven less than twice the perimeter of the given triangle. Twice the perimeter of the given triangle is $2P = 2(7y + 8)=14y+16$. Seven less than this is $14y+16 - 7$.

Step3: Simplify the expression for the new perimeter

$14y+16 - 7=14y + 9$.

Answer:

$14y + 9$