Question

The three sides of a right triangle form a geometric sequence. What is the ratio of the length of the shortest side to the length of the hypotenuse? Express your answer as a decimal to the nearest tenth.

Answer 1

@jim_thompson5910

Answer 2

http://cdn.shopify.com/s/files/1/0063/3802/files/Squares_Square_Root_Pythagorean_2_grande.jpg

Answer 3

btw, is there a picture you'd want to show us?

Answer 4

No, there is no pic
:(

Answer 5

Sorry, I am not sure about the link you sent...

Answer 6

@satellite73

Answer 7

Now I kinda understand the link, jdoe

Answer 8

problem is, I don't have any measurements

Answer 9

the exercise assumes there is a "shortest side" and a ratio to the hypotenuse, and expects a rounded answer, thus there's some right angle we're not seeing

Answer 10

um...

Answer 11

does anyone have an idea how to solve or does anyone think it's imposs?

Answer 12

lets say the three lengths are a , ar and ar^2
then required ratio is a / ar^2 = 1 / r^2

also a^2r^4 = a^2 + a^2r^2
r^4 = r^2 + 1
let R = r^2
R^2 - R - 1 = 0
R = r^2 = 1.618

ratio = 1 /1.618

i think thats right

Answer 13

Wow! You actually did that!

Answer 14

i think i understand now...thx

Answer 15

i'll look it over but it looks reasonable to me:)

Answer 16

- I used formula for terms of a GP and also Pythagoras

this only applies when the right angles triangle has different lengthed sides

Answer 17

yea i think it makes sense

Answer 18

I noticed the Pythagoras

Answer 19

what's gp stand for?

Answer 20

GP

Answer 21

suppose we take a to be 2 and work out ar and ar^2
and see it they fir
GP = gemetric progression ( or series)

Answer 22

(or sequence) yep

Answer 23

yes

Answer 24

if a = 2

the 3 sides will have length 2, 2*sqrt1.618 and 2*1.618

by pythagoras

(2*1.618)^2 = 2^2 + (2*sqrt1.618)^2
10.472 = 10.472


it checks out