Staircase 5322

Find out if the handrail on a staircase with 20 steps will be longer than 7 m if the step is 32 cm wide and 15 cm high. (1 = Yes, 0 = No)

Correct answer:

x =  1

Step-by-step explanation:

$$\begin{gathered} n=20 \\ x=32\text{cm}\to \text{m}=32:100\text{m}=1\text{m} \\ y=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ a=n\cdot x=20\cdot 1=\frac{32}{5}=6\frac{2}{5}=6.4\text{m} \\ b=n\cdot y=20\cdot 0.15=3\text{m} \\ c=\sqrt{a^2+b^2}=\sqrt{6.4^2+3^2}\doteq 7.0682\text{m} \\ c>7m \\ x=1 \end{gathered}$$

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