Question

Rectangles A and B are similar rectangles. The length of the diagonal of Rectangle A is 13 inches and the length of the diagonal of Rectangle B is 6.5 inches.

What could be the length and width of both Rectangle A and Rectangle B? Show your work.

Rectangle A: 5 in x 12 in, Rectangle B: 2.5 in x 6 in

Rectangle A: 6.5 in x 14 in, Rectangle B: 3.5 in x 8 in

Rectangle A: 4 in x 10 in, Rectangle B: 3 in x 7 in

Rectangle A: 7 in x 11 in, Rectangle B: 2 in x 5 in

Answer 1

tips

Answer 2

ratio of the sides should be the same.

Answer 3

so

Answer 4

ehh

Answer 5

ehh

Answer 6

rectangle A

Answer 7

choice 1

Answer 8

choice 1

Answer 9

30=30

Answer 10

\[\frac{13}{6.5} = 2\]
Check the ratio of the corresponding sides now.
For example, for option A, the first pair = 5/2.5 = 2 => true

Answer 11

so am I right?

Answer 12

30=30 for choice 1?

Answer 13

How do you get 30?
*Note I don't mind if you don't type eh twice. It lengthens the post and possibly makes my computer slow if you continue.

Answer 14

easy, 5/12=2.5/6

Answer 15

you see it now?

Answer 16

12 times 2.5=30 and 5 times 6=30

Answer 17

did I do something wrong?

Answer 18

you see what I am saying?

Answer 19

what do you think, KingGeorge?

Answer 20

Oh... you're equating them and show they are equal. Weird to me :|
But option 1 is the right choice. Simply because the corresponding sides share the same ratio.
Given:\[\frac{ diagonal \ of \ rectangle \ A}{ diagonal \ of \ rectangle \ B} = \frac{13}{6.5} = 2\]Now, for option 1
\[\frac{Length \ of \ rectangle \ A}{Length \ of \ rectangle \ B} = \frac{5}{2.5} = 2\]\[\frac{Width \ of \ rectangle \ A}{Width \ of \ rectangle \ B} = \frac{12}{6} = 2\]
=> similar!

Answer 21

d=so I was right?

Answer 22

you just cross multiply

Answer 23

I didn't cross multiply. I'm not sure if your method is right, but that doesn't make sense to me..

Answer 24

is it, KingGeorge?

Answer 25

@luisz your method will not always give the correct solution. In this case, it works because the other options they provided you with are not similar rectangles.

Answer 26

If you cross multiply the other ratios, they will not equate

Answer 27

ahh

Answer 28

You can use that method to show similarity between two rectangles, but their ratio of similarity may not be what you wanted.

Answer 29

I see

Answer 30

y

Answer 31

ty

Answer 32

next problem