Question

There is a staircase as shown in the given figure, connecting point A, B. measurements of the step are marked in the figure. Find the straight line distance between A and B.

Answer 1

If you observe we can see that there is a large right triangle formed with the combined lengths of the other two sides of the triangle.

Extend the bottom-most triangle's base and topmost triangle's $1.8unit$ side till they touch each other at $C$.

$\Rightarrow$ $AC=2+2+2+2=8unit$

$\Rightarrow$ $BC=1+1.6+1.6+1.8=6unit$

$\therefore$ $A{B}^2=A{C}^2+B{C}^2$ [ By Pythagoras theorem ]

$\Rightarrow$ $A{B}^2=(8{)}^2+(6{)}^2$

$\Rightarrow$ $A{B}^2=64+36$

$\Rightarrow$ $A{B}^2=100$

$\therefore$ $AB=10unit$