Three consecutive even integers have a sum of 48 . find the integers.

x+(x+2)+(x+4)=48

3x+6=48

Minus 6 to both sides

3x=42

Divide 3 to both sides

x=14

Get the next two integers

x,x+2,x+4 or 14,16,18 = 48 is you Answer

i'm sure goog can you get that answer

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