Is this set of ratios equal? : 1/2 and 12/24

1/2

12/24 -1/2 ( divide by 12)

12/12= 1 , 24/12= 2

1/2 and 12/24 are equal

These sets are equal. First, 12/24 is still dividable. So when we divide to the max point, we have to divide 12/24 by 12 and will get 1/2. So that is equal. And 12/24 is the same as 0.5 and 1/2 is 0.5 as well.

So, in conclusion, 12/24 is the same as 1/2.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4