Triangular Island has a lighthouse at each of its corners, N, O, and B. The perimeter of Triangular Island is 5.2 miles. There is a channel on Triangular Island which is parallel to BO and divides it into two smaller islands: Green Island and Coconut Island. The length of the channel is equal to half of the distance between the lighthouses on Coconut Island. What is the perimeter of Green Island?

answer: ouch. thats difficult

step-by-step explanation:

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

i think the answer is 90 hope this