Question

Assistance needed :)


You originally draw a design for an art contest on a 2 in. x 5 in. card. The second phase of the contest requires the drawing to be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.

Answer 1

I'm a bit confused on what it wants me to do.

Answer 2

I'm guessing that if it is 10.5 I need to find the scale factor to find the tiny dimension?

Answer 3

So think about it like this

Here are 2 rectangles and I tell you they are similar



What does similar mean? It means we can go from the smaller figure to the bigger figure by finding how just how much bigger it really is

Andddddd you beat me to it with that last comment :P

Yes you need the scale factor

Answer 4

Oh okay haha XD

Answer 5

Can you help me find the scale factor? I always struggle with it

Answer 6

This problem can be set up as a ratio, I think...

Answer 7

If 10.5 is your largest side...
2 is to 5 as x is to 10.5

Answer 8

Think about it as a proportion

\[\large \frac{2}{5} = \frac{x}{10.5}\]

solve for 'x'

Answer 9

Cross multiply right?

Answer 10

Correct

Answer 11

Yes

Answer 12

2 • 10.5 = 21
5 • x = It needs to be 21 so I divide 21 by 5 right?
I got 4.2

Answer 13

And that is correct :)

Answer 14

So to write it to the nearest tenth I just write 4, and that will be m answer?

Answer 15

Nope, that .2 is the tenths spot! 4.2 is your full answer

Answer 16

Ah okay :)

Answer 17

If it said round to the nearest integer or to the nearest whole number...that would be 4 :)

Answer 18

Thank you :D

Answer 19

They require utilize as much of the space on the paper as possible but 4.2 is less than half of 8.5

Answer 20

@Secret-Ninja

Answer 21

Confusing math

Answer 22

You're right, they do want to utilize as much space as possible, but in order to keep the drawing from being distorted, they need to keep the images similar

So we found the scale factor to be 2.1

5 times 2.1= the 10.5 they gave us
and
2 times 2.1 = the 4.2 we found to be the answer

Answer 23

Yes that is also correct that's why I call it confusing.

Answer 24

Don't worry guys I got it right. :)