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

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

part 33)
`P=1.5x\ units`

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=(x)/(4)\\BC=(x)/(2)\\DE=(x)/(4)-y\\FG=y\\HA=(x)/(4)`

substitute the given values

`P=(x)/(4)+(x)/(2)+CD+(x)/(4)-y+EF+y+GH+(x)/(4)`

Combine like terms

`P=(5)/(4)x+CD+EF+GH`

we know that

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

so

`CD+EF+GH=AB=(x)/(4)`

substitute in the formula of perimeter

`P=(5)/(4)x+(x)/(4)=(6)/(4)x`

Simplify

`P=(3)/(2)x=1.5x\ units`