Bob takes the subway to work and uses an escalator at the railway station. if bob runs up 8 steps of the escalator, then it takes him 46.5 seconds to reach the top of the escalator. if he runs up 13 steps of the escalator, then it takes him only 39.0 seconds to reach the top. how many seconds would it take bob to reach the top if he did not run up any steps of the escalator

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

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to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.