Matthew helps to paint another wall. He puts painter's tape on the floor along this wall as well, he puts down 218 centimeters of tape. Beginning at the right end of the wall, he puts down 110 centimeters of tape. The two pieces of tape are too short to connect. He needs to place a third piece of tape between the two other pieces so that tape is along the entire wall. Solve for the length of the third piece of tape, in centimeters. SHOW YOUR WORK

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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

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: