Question

In the figure, the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD is ___ . The area of polygon ABCDE is ___ square units.

part 1 options
2/3
1
3/2
2
Part 2 options
18
22
24
28

Please help me I cant figure this out to save my life and I need to finish by tomorrow or I can't go on my senior trip. I'll fan and give anyone a medal that can help me!

Answer 1

https://cdn.ple.platoweb.com/EdAssets/35d21e00057140ab829a717857a217fa?ts=635375425111030000 < link to figure

Answer 2

were you able to find the perimeter of rectangle ABDE?

Answer 3

32?

Answer 4

what is the base of the rectangle? I.e, what is the distance from D to E?

Answer 5

2

Answer 6

yep, how about the height? what is the distance from E to A?

Answer 7

6
so the perimeter of the rectangle is 12?

Answer 8

the rectangle ABDE looks like this

Answer 9

add up the four sides
2+6+2+6 = 8+8 = 16

Answer 10

so the perimeter of ABDE is 16 units

do you agree with this statement?

Answer 11

yes

Answer 12

ok now onto the triangle

Answer 13

how long is segment BD?

Answer 14

6

Answer 15

yes

Answer 16

to find the other 2 sides, we will need to use the distance formula

have you learned this formula in your lesson?

Answer 17

Not that I found

Answer 18

have you learned the pythagorean theorem?

Answer 19

a^2 + b^2 = c^2?

Answer 20

yes

Answer 21

so we start with this

https://cdn.ple.platoweb.com/EdAssets/35d21e00057140ab829a717857a217fa?ts=635375425111030000

what I would do next is draw in red segments as you see in the attached document

Answer 22

based on this

http://assets.openstudy.com/updates/attachments/574e2196e4b056c4b3e61ce0-jim_thompson5910-1464740094550-triangle1.jpg

how long is the green segment? how long is the red segment?

Answer 23

4 and 3

Answer 24

very good

Answer 25

focus on that triangle and we see this

Answer 26

to find the distance from D to C is the same as finding the hypotenuse x

Answer 27

in this case

a = 4
b = 3
c = x

c is always the longest side

Answer 28

do you know how to use this info to find the value of c?

Answer 29

I honestly have no idea.
would that still be 6 or no?

Answer 30

\[\Large a^2+b^2 = c^2\]
\[\Large 4^2+3^2 = x^2\]
\[\Large 16+9 = x^2\]
\[\Large 25 = x^2\]
\[\Large x^2 = 25\]


If x^2 = 25, then x = ???

Answer 31

5?

Answer 32

yes, so the distance from D to C is 5 units

this is the same as saying segment DC is 5 units long

Answer 33

now draw in additional segments to form another right triangle

Answer 34

what are the lengths of those vertical and horizontal segments?

Answer 35

3 and 4?

Answer 36

yes, so how long is BC?

Answer 37

5 units?

Answer 38

yep

Answer 39

to summarize triangle BCD, so far, we have

BD = 6
DC = 5
BC = 5

what is the perimeter of triangle BCD?

Answer 40

16?

Answer 41

yes

Answer 42

the perimeter of rectangle ABDE is 16 units

the perimeter of triangle BCD is 16 units

Answer 43

so the answer is 1?

Answer 44

to find `the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD`

we divide the two values

ratio = (perimeter of rectangle)/(perimeter of triangle) = 16/16 = 1

Answer 45

yes the answer to the first part of the question is 1

Answer 46

so is the second part 24?

Answer 47

let me check

Answer 48

You nailed it. Nice job.