Question

6.1 simplify the expressions find the perimeter (add up all sides) ① ② ③ ④ ⑤

Explanation:

Step1: Sum all rectangle sides

$P = (2x+1) + (3x) + (2x+1) + (3x)$

Step2: Combine like terms

$P = (2x+3x+2x+3x) + (1+1) = 10x + 2$

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Step1: Sum all triangle sides

$P = 2x + 3x + 4x$

Step2: Combine like terms

$P = (2+3+4)x = 9x$

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Step1: Sum all rectangle sides

$P = (2y-3) + 4y + (2y-3) + 4y$

Step2: Combine like terms

$P = (2y+4y+2y+4y) + (-3-3) = 12y - 6$

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Step1: Note visible sides (complete 2 sides missing, use shown ones)

$P = (2x-1) + 5 + 5$

Step2: Combine like terms

$P = 2x + (-1+5+5) = 2x + 9$

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Step1: Sum all rectangle sides

$P = (x+3) + (2x+4) + (x+3) + (2x+4)$

Step2: Combine like terms

$P = (x+2x+x+2x) + (3+4+3+4) = 6x + 14$

Answer:

1. $10x + 2$
2. $9x$
3. $12y - 6$
4. $2x + 9$ (using visible sides)
5. $6x + 14$