A builder makes staircases where each step is 28/,/text{cm}28cm28, start text, c, m, end text long and rises 18/,/text{cm}18cm18, start text, c, m, end text so people don't trip. Every staircase has a stringer - a diagonal support connecting all of the steps. A certain staircase will have 666 steps. What is the length / ellℓell of the stringer for this staircase? Round your answer to the nearest tenth of a centimeter. / text{cm}cmstart text, c, m, end text

Question

Mathematics

Sammy Wise

11 November, 12:09

A builder makes staircases where each step is 28/,/text{cm}28cm28, start text, c, m, end text long and rises 18/,/text{cm}18cm18, start text, c, m, end text so people don't trip. Every staircase has a stringer - a diagonal support connecting all of the steps. A certain staircase will have 666 steps. What is the length / ellℓell of the stringer for this staircase? Round your answer to the nearest tenth of a centimeter. / text{cm}cmstart text, c, m, end text

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Answers (2)

Know the Answer?

Casper · Answer 1

Each step has a diagonal aka hypotenuse h that satisfies

h² = 28² + 18² = 1108

The total length of 666 diagonals is

l = 666h = 666 √1108 ≈ 22168.898213488195

Answer: 22168.9 cm

Roland Wilcox · Answer 2

The length of the stringer ℓ is approximately 199.7m