Find the perimeters of a Pentagon and Octagon?

Question

A pentagon with all 5 sides the same size has the same perimeter as an octagon in which all 8 sides are the same size. One side of the pentagon is 2 less than 3times the length of one side of the octagon. Find the perimeters.

I know the formula is 3-2x = something.... Do i multiply this formula by 8 and 5 and have it equal each other? showing 8(3-2x)=5(3-2x) or am i going about this totally incorrectly? I love when I'm given math problems and there's no reference in the book as to what the perimeter of an octagon or pentagon is. I did search online and found that the sum of all 5 sides of a pentagon is the perimeter and same goes for octagon where the sum of all 8 sides = the perimeter.

Answer 1

Hi Karen,

It's good that you tried to do your problems. Some ppl just post stuff on yahoo! answers, without trying, to get their answer.

Anyway, This is how you would do you problem. Belive me it's that tough.

Definition of Perimeter=sum of all sides.

X=one side of pentagon
Y= one side of octagon

Given-
5X=8Y
X=3Y-2

Now substitute X=3Y-2 into 5X=8Y to find Y.

So...5(3Y-2)=8Y
15Y-10=8Y
7Y=10
Y=10/7

Substitute Y=10/7 into X=3Y-2 to find what X is.
so...X=3(10/7)-2
X = (30/7)-2
X=16/7

Enjoy!

Answer 2

in case you upload 5 equivalent components,y, of a pentagon, the sum is the fringe. in case you upload 8 equivalent components,x, of the octagon, that sum is the fringe of the octagon. to discover the perimeters, first call one area of the octagon x. the fringe of the octagon is subsequently 8x. the fringe of the pentagon is an identical, so this is 8x too. in spite of the undeniable fact that this is provided that one area of the pentagon y, is y= 3x-2 because of the fact that a pentagon is 5 sided, its perimeter is 5y. exchange 3x-2 for y. P=5y=5(3x-2)=15x-10 undergo in concepts this is an identical perimeter as P for the octagon. so---- 15x-10=8x 7x-10=0 7x=10 x=10/7 this is the dimensions of one area of the octagon. the fringe P=8x=8(10/7)=80/7=11 3/7 permit's see if this works for the pentagon. y=3x-2=3(10/7)-2 =(30/7)-(14/7)=sixteen/7 P=5y=5(sixteen/7)=80/7=11 3/7 Correctomundo. x=10/7 y=sixteen/7 and P=80/7=11 3/7

Answer 3

If you add five equal sides,y, of a pentagon, the sum is the perimeter.
If you add eight equal sides,x, of the octagon, that sum is the perimeter of the octagon.

To find the perimeters, first call one side of the octagon x.
The perimeter of the octagon is thus 8x.
The perimeter of the pentagon is the same, so it is 8x too.
But it is given that one side of the pentagon y, is
y= 3x-2
Since a pentagon is five sided, its perimeter is 5y.
Substitute 3x-2 for y.
P=5y=5(3x-2)=15x-10
Remember this is the same perimeter as P for the octagon.
so---- 15x-10=8x
7x-10=0
7x=10
x=10/7
This is the length of one side of the octagon.
The perimeter P=8x=8(10/7)=80/7=11 3/7
Let's see if this works for the pentagon.
y=3x-2=3(10/7)-2
=(30/7)-(14/7)=16/7
P=5y=5(16/7)=80/7=11 3/7
Correctomundo.
x=10/7 y=16/7 and P=80/7=11 3/7

Answer 4

Let,each side of the octagon be x,Therefore the length of each side of the pentagon is 3x-2. So according to the problem,we get 5(3x-2)=8x => 15x-10=8x =>15x-8x=10 =>7x=10 =>x=10/7=1 3/7 .Therefore,length of each side of the octagon is 1 3/7 and that of the pentagon is (10/7)x3-2=2 2/7.