Question

1. write the perimeter of the rectangle as a simplified expression.
2. write the perimeter of the triangle as a simplified expression.

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=7x + 1$ and $w=x - 3$.
\[P=2((7x + 1)+(x - 3))\]

Step2: Simplify the expression inside the parentheses

\[P=2(7x+1 + x - 3)=2(8x - 2)\]

Step3: Distribute the 2

\[P = 16x-4\]

Step4: Recall perimeter formula for triangle

The perimeter $P$ of a triangle is the sum of its side - lengths. The side - lengths are $y - 4$, $3y + 5$, and $6y$.
\[P=(y - 4)+(3y + 5)+6y\]

Step5: Combine like terms

\[P=y-4 + 3y+5 + 6y=(y + 3y+6y)+(-4 + 5)=10y + 1\]

Answer:

1. The perimeter of the rectangle is $16x-4$.
2. The perimeter of the triangle is $10y + 1$.