Question

Are the answers 8 and 10?

Answer 1

I think so.

Answer 2

how do you come to 8 and 10?

Answer 3

18+9 = 27, not 29

Answer 4

I thought those are 30-60-90 Triangles, so the hypotenuse would be twice the short side.

Answer 5

How is the answer 27?

Answer 6

the perimeter is 29

4+5+10+8 = 27, not 29

Answer 7

why would you think its a 30-60-90? nothing indicates to me that that is the case

Answer 8

Ok...then how do I find AC and AB?

Answer 9

still working on that ... do you ahve options?

Answer 10

No options

Answer 11

hmm, all i know at the moment is that 10 and 8 dont work out for the stated perimeter. do you agree?

Answer 12

do we know law of sines?

Answer 13

Yes, 10 and 8 don't work

Answer 14

But there are no angles for the Law of Sines

Answer 15

im wondering if we can use them in a general sense tho, i havent got a clear approach yet.

Answer 16

other than assuming a 30=60-90 what else are you thinking of?

Answer 17

I'm wondering if we can use this theorem: An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the two other sides.

Answer 18

sounds reasonable:

so the ratio is 5:4, therefore

5k + 4k + 9 = 29

what is k?

Answer 19

k is 2.2

Answer 20

i was working out something like

sin(a')/5 = sin(c)/(ad)
sin(a')/4 = sin(b)/(ad)

(ad) sin(a') = 5sin(c)
(ad) sin(a') = 4sin(b)

5 sin(c) = 4 sin(b)

sin(b)/4 = sin(c)/5 = sin(a)/9

Answer 21

20/9 is a more exact number

Answer 22

(5(20)+ 4(20) + 81)/9

(180 + 81)/9

261/9 = 29 of course

Answer 23

Ok. Thanks!

Answer 24

as long as your thrm is good, that should be it ... me and geometry thrms are not on speaking terms :)