Trigonometry i need to find the perimeter of the triangle

so, the bottom-left angle is 60°, and the bottom-right angle is 60° as well, that simply means the angle up above is also 60°, meaning, this is an equilateral triangle.

step-by-step explanation: 4 cause 2+2=4

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