Question

Choose the correct answer from the alternatives given.
The upper end of a ladder touches a $12$ meter high window on one side of a street. The ladder is rotated to opposite side of the street keeping its foot fixed and touches a $9$ meter high window. If the length of the ladder is $15$ m, then find the width of the road.

• A. $15m$
• B. $9m$
• C. $21m$
• D. $12m$

Answer 1

Answer: (C)

$21m$

Let ladder = BC = CD $15$ meter
B and D are windows on opposite sides of street.
Given, $DE=9$ meter
$AB=12$ meter Given, $DE=9$ meter
In right angled $\Delta$ BAC,
$A{C}^2+A{B}^2=B{C}^2$
$A{C}^2+122=152$
AC+ $144=225$
$A{C}^2$ = 225 $144=81$
AC = $\sqrt{81}$ = 9 metres
In $\Delta$ CED
Similarly,$CE=\sqrt{{15}^2-9^2}=\sqrt{225-81}=\sqrt{144}=12$ metre.
$\therefore$ Width of the road $AE=AC+CE=9+12=21$ metre