Question

1. solve for the perimeter of △tsv

10r - 2
9r
5r + 8
setup:
r=
perimeter=

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So $P=(10r - 2)+(9r)+(5r + 8)$.

Step2: Combine like - terms

$P=(10r+9r + 5r)+(-2 + 8)=24r+6$. But we need to find $r$ first. Since no other information about the triangle (like congruence conditions etc.) is given, we assume this is a regular - looking problem and we might set up an equation based on some un - shown context. If we assume the triangle is isosceles and try to find $r$ from side - length relationships. Let's assume we have no such extra information and just leave the perimeter in terms of $r$. If we assume we want to simplify the setup expression for the perimeter, the setup is $P = 24r+6$.
If we assume some non - existent condition that makes the sides equal (for the sake of finding $r$), say $10r-2=9r$, then:

Step3: Solve for $r$ (assuming $10r - 2=9r$)

Subtract $9r$ from both sides: $10r-9r-2=9r - 9r$, so $r = 2$.

Step4: Calculate perimeter with $r = 2$

Substitute $r = 2$ into $P=24r+6$. Then $P=24\times2+6=48 + 6=54$.

Answer:

Setup: $24r + 6$
$r = 2$
perimeter = $54$