3/5+1/2 in simplest form

Step-by-step explanation:

1. find common denominator

so 3/5 is 6/10 and 1/2 is 2/10

2. add to make 8/10

3. simplify to 4/5 as they're both divisible by 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