Alex, bob, and claudia split 126 cm wire evenly among themselves. they then proceeded to cut their pieces of wire into smaller, equal parts. alex cut his wire 18 times, and kept 7 pieces. bob cut his wire 2 times more than alex did, and kept 9 pieces. while claudia divided her wire into 13 equal parts, and kept only one piece. who kept the longest part of the original wire and what was the length of that part?

Bob18 cmStep-by-step explanation:

If Alex cut his wire 18 times, he ended up with 19 equal pieces. He kept 7, so has 7/19 of his 1/3 of the wire.

Bob cut his wire 20 times, so ended up with 21 pieces, of which he kept 9. So he has 9/21 = 3/7 of his 1/3 of the wire.

Claudia kept 1/13 of her 1/3 of the wire, so has the smallest piece.

Bob kept (3/7)·(1/3)·126 cm = 18 cm.

Alex kept (7/19)·(1/3)·126 cm ≈ 15.47 cm.

Bob kept the longest part of the original wire.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Dwould be the answer