When two pieces of rope are placed end to end, their combined length is 122 feet. when the two pieces
are placed side by side, one is 36 feet longer than the other. what is the length of the longest piece of
rope?

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step-by-step explanation:

just took the test and my answers down below!

step-by-step explanation:

check the pic :

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen

your answer is #3 , 8 - 3 square root of 11