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Diagonals of a Rectangle Bisect Each-Other and Are Equal

A ladder 20...

Question

A ladder $20$ m long is placed in a street, so as to reach a window $16$ m high and on turning the ladder to the other side of the street it reaches a point $12$ m high. What is the width of street?

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Solution

$O Q^{2} = O L^{2} - L Q^{2}$
$= 20^{2} - 16^{2}$
$= 144$
$O Q = 12$
Again $O P^{2} = 20^{2} - 12^{2} = 256$
OP=16
Thus width of the road
=OP+OQ
=16+12=28m

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