Question

A ladder 25 m long reaches a window at a height of 7 m above the ground. Keeping its foot at the same point, the ladder is turned so that it reaches a window 20 m high across the street. Find the total width of the street.​

Answer 1

$\huge\bf\underline{\underline{Question:}}$

A ladder 25 m long reaches a window at a height of 7 m above the ground. Keeping its foot at the same point, the ladder is turned so that it reaches a window 20 m high across the street. Find the total width of the street.

$\huge\bf\underline{\underline{Solution:}}$

Lets assume that BD is the street,AC and EC is ladder and AB and ED are walls.

AC = EC = 25m

AB = 7m

ED = 20m

In $\triangle$ABC,$\angle$B = 90°

By Pythagoras theorem

$AB^2+BC^2=AC^2\\7^2+BC^2=25^2\\49+BC^2=625\\BC^2=625-59\\BC^2=576\\BC=\sqrt{576} \\BC=24$

In $\triangle$ECD,$\angle$D = 90°

By Pythagoras theorem

$CD^2+ED^2=EC^2\\CD^2+20^2=25^2\\CD^2+400=625\\CD^2=625-400\\CD^2=225\\CD=\sqrt{225} \\CD=15$

Width of the street = BC + CD

Width of the street = 24 + 15

Width of the street = 39 metres

Therefore, the width of the street is 39 metres.

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@ItsMysteriousGirl