Question

Simplified polynomial expression for the permiter of each figure. Could someone help me how to do that step by step or recommend me a video to watch so I could understand.

Answer 1

Answer:

part 32) $P=2a+4b+3c\ units$

part 33) $P=1.5x\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Part 32) we know that

The perimeter of the figure is equal to the sum of its length sides

$P=AB+BC+CD+DE+EF+FG+GH+HA$

we have

$AB=2b+2c\\BC=c\\DE=a-c\\EF=b+c\\FG=3b\\GH=c\\HA=a-3b$

substitute the given values

$P=(2b+2c)+c+CD+(a-c)+(b+c)+3b+c+(a-3b)$

Combine like terms

$P=3b+4c+2a+CD$

Find the value of CD

we know that

AB=CD+EF+GH ----> by segment addition postulate

substitute

$2b+2c=CD+b+c+c\\2b+c=CD+2c+b\\CD=b-c$

substitute  in the formula of perimeter

$P=3b+4c+2a+b-c\\P=2a+4b+3c$

Part 33) we know that

The perimeter of the figure is equal to the sum of its length sides

$P=AB+BC+CD+DE+EF+FG+GH+HA$

we have

$AB=\frac{x}{4}\\BC=\frac{x}{2}\\DE=\frac{x}{4}-y\\FG=y\\HA=\frac{x}{4}$

substitute the given values

$P=\frac{x}{4}+\frac{x}{2}+CD+\frac{x}{4}-y+EF+y+GH+\frac{x}{4}$

Combine like terms

$P=\frac{5}{4}x+CD+EF+GH$

we know that

$AB=CD+EF+GH$----> by segment addition postulate

so

$CD+EF+GH=AB=\frac{x}{4}$

substitute  in the formula of perimeter

$P=\frac{5}{4}x+\frac{x}{4}=\frac{6}{4}x$

Simplify

$P=\frac{3}{2}x=1.5x\ units$