Question

The circle is tangent to the outer reactangle, and touches the corners of the inner reactangle. The area of the inner reactangle is 80/
1. find the area of the outer reactangle witout using algebra. It is possible to look at the picture and immediately tell what the area is

Answer 1

wait let me attach the image

Answer 2

rectangle must be a square right?

Answer 3

it says rectangle here and in the image it looks square but it's sayign reactnagle

Answer 4

oh nvm i have no idea, i suck at geometry

Answer 5

:( @jim_thompson5910

Answer 6

@satellite73 man you are no help. shame shame

Answer 7

ok lets do it

Answer 8

it is tangent to the circle , so it is a square
both are squares

Answer 9

sorry I was drawing it out, but go ahead @satellite73

Answer 10

inside one has area 80 so the length of the side is \(\sqrt{80}\)

Answer 11

okay @jim_thompson5910 it's okay! and @satellite73 show your powers! you got it!

Answer 12

this*

Answer 13

that means the length of the diameter of the circle is \(\sqrt{80}\times \sqrt{2}=\sqrt{160}=4\sqrt{10}\)

Answer 14

that is therefore the length of the side of the larger rectangle

Answer 15

and so its area is \(160\)
now i just made that up as you might can tell
if @jim_thompson5910 has a better (aka correct) solution please post it

Answer 16

btw not sure if i "used algebra" or not

Answer 17

okay let's see what @jim_thompson5910 say I will decide the winner lol

Answer 18

apparently, if i did not screw up, the area is twice as large

Answer 19

hmmm

Answer 20

the suspense is killing me!!

Answer 21

yeah the answer is 160

here's how I did it

r = radius of circle
use the pythagorean theorem or the 45-45-90 triangle template to find that r/(sqrt(2)) = r*sqrt(2)/2 is half the side of the smaller square, so r*sqrt(2) is the side of the square

area of smaller square = (r*sqrt(2))^2 = 2r^2

the larger square has area equal to 2r*2r = 4r^2

ratio of larger square to smaller square = (4r^2)/(2r^2) = 2

so basically

area of larger square = 2*(area of smaller square)

Answer 22

how the teacher thinks that it's obvious without using algebra, I have no clue

Answer 23

i think we did basically the same thing
i just asserted that if the sides is \(\sqrt{80}\) then the diagonal is \(\sqrt{160}\)

Answer 24

yeah pretty much

Answer 25

okay I will write both method ans ask my teacher which one will be best :) tysm you both are so nice

Answer 26

and your teacher will say "stop cheating and DIY"!

Answer 27

I will medal @jim_thompson5910 this time I guess you both don't care u got enough gold

Answer 28

no @satellite73 y teacher is nice not like u mr.meany

Answer 29

that is for sure
i traded in my first 1000 for the bike in my picture, but the rest are apparently useless