Question

Walls of two buildings on either side of a street are parallel to each other. A ladder $5.8$ m long is placed on the street such that its top just reaches the window of a building at the height of $4$m. On turning the ladder over to the other side of the street, its top touches the window of the other building at a height $4.2$ m Find the width of the street.

Answer 1

By pythagoras theorem,

${5.8}^2=x^2+{4.2}^2$

and ${5.8}^2=y^2+4^2$

$\Rightarrow x=\sqrt{{5.8}^2-{4.2}^2}=\sqrt{\left(10\right)\left(16\right)}=\sqrt{16}=4$

$y=\sqrt{{5.8}^2-4^2}=\sqrt{9.8\times 1.8}=4.2m$

$\Rightarrow$ width $=x+y=8.2m$