Question

Tom photocopied the image of a design for a monorail track system. The figure below shows the design and its photocopy.

Two irregular quadrilaterals ABCD and EFGH are drawn. EFGH is the photocopy of design ABCD. AB measures 17 meters, AD measures 7 meters. No dimensions are shown on EFGH.

The ratio of BC : CD is 2 : 3. The total length of track on the design is 49 meters. What is the length, in meters, of side GH on the photocopied image?

Answer 1

for the design, you know the perimeter is 49m
so

49=7+17+BC+CD

you also know
BC:CD=2:3 or BC/CD=2/3

Answer 2

25=BC+CD
and
you know the ratio of the other two sides so use a variable like x to solve the sides

Answer 3

know what to do next?

Answer 4

how did you get 25.?

Answer 5

nm 49-24

Answer 6

25=BC+CD
25=2x+3x=5x, therefore x*5
since BC=2x and CD=3x, then BC=10 and CD=15
BC/CD=10/15=2/3 like the problem said

49=7+17+BC+CD
49=7+17+10+15, so it's right

Answer 7

How did I get 25?

49=7+17+BC+CD
49=24+BC+CD
25=BC+CD

Answer 8

I'm a little lost... :/ I'm so sorry lol

Answer 9

how would you find the side length GH.....?

Answer 10

it gives you the perimeter=49
total length of track on the design is 49
that's the sum of all the sides
it gives you AB and AD but not BC and CD
to find BC and CD, you use the ratio given being 2/3

Answer 11

so do 2/3=49/x to find side length GH..?

Answer 12

it's a photocopy, so it's the same size

Answer 13

so FG=BC

Answer 14

whoops, I meant GH=CD

Answer 15

I'm completely missing something..What is wrong with me! Geesh I'm so sorry.

Answer 16

OOOH! So it'd be 15.?

Answer 17

yeah

Answer 18

WWOOOOHHOOO!

Answer 19

Your awesome!! Thank youu!!