Question

Quadrilateral ABCD in the figure below represents a scaled-down model of a walkway around a historic site. Quadrilateral EFGH represents the actual walkway. ABCD is similar to EFGH.

Two irregular similar quadrilaterals ABCD and EFGH are drawn. AB measures 6 inches, BC measures 3 inches, CD measures 3 inches and DA measures 4 inches. EF measures 72 feet.

What is the total length, in feet, of the actual walkway?

Answer 1

Is this what it looks like?

Answer 2

yes

Answer 3

First off, we know ABCD and EFGH are similar

Answer 4

The only difference is they're scaled differently

Answer 5

We know that the ratio between each corresponding segment will be the same.

Answer 6

we also know that AB is 6 inches, and that EF is 72 feet

Answer 7

wait, so how do i find the sides on the bigger shape

Answer 8

We have to use what we already know about the smaller shape to find the sides of the bigger one

Answer 9

hmm, so everything on the smaller shape is half of the bigger shape?

Answer 10

like if they divided the numbers in half

Answer 11

Not quite,

Answer 12

Okay, as I said earlier we know the ratio between each corresponding segment will be the same. and that EF is 72 feet, so the ratio is 144 (72/6 = 12, then 12 inches per foot) Meaning EF is 12 times longer (in feet) than AB is (in inches)...

Answer 13

Are you following?

Answer 14

yes, so then GF would be 36 because it would also be 12 time longer then CB?
because AB times 12 get you 72 which is EF

Answer 15

Yeah, here: are the steps
EF = 72 ft

FG = 36 ft (3 * 12)

GH = 36 ft (3 * 12)

EH = 48 ft (4 * 12)

Answer 16

So, now we know that the total length of the pathway is: 72 + 36 + 36 + 48 = 192 feet

Answer 17

oh, okay i get it now, thank you!

Answer 18

Np! can I get a medal?

Answer 19

how do i do that

Answer 20

Thank you!