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Home » 7. The foot of a ladder is     away from a wall and its top reaches a window     above the ground. If the ladder is shifted in such a way that its foot is     away from the wall, to what height does its tip reach?
7. The foot of a ladder is

    \[\mathbf{6}\text{ }\mathbf{m}\]

away from a wall and its top reaches a window

    \[\mathbf{8}\text{ }\mathbf{m}\]

above the ground. If the ladder is shifted in such a way that its foot is

    \[\mathbf{8}\text{ }\mathbf{m}\]

away from the wall, to what height does its tip reach?
CBSE | Class 10 | Maths | RD Sharma | Triangles | Triangles
7. The foot of a ladder is

    \[\mathbf{6}\text{ }\mathbf{m}\]

away from a wall and its top reaches a window

    \[\mathbf{8}\text{ }\mathbf{m}\]

above the ground. If the ladder is shifted in such a way that its foot is

    \[\mathbf{8}\text{ }\mathbf{m}\]

away from the wall, to what height does its tip reach?

Solution:      

Let’s assume the length of ladder to be, AD = BE = x m

So, in ∆ACD, by Pythagoras theorem

We have,

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> A{{D}^{2}}~=\text{ }A{{C}^{2}}~+\text{ }C{{D}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow {{x}^{2}}~=\text{ }{{8}^{2}}~+\text{ }{{6}^{2}}~\ldots \text{ }\left( i \right) \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

                                                        

    \[\]

Also, in ∆BCE, by Pythagoras theorem

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> B{{E}^{2}}~=\text{ }B{{C}^{2}}~+\text{ }C{{E}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow {{x}^{2}}~=\text{ }B{{C}^{2}}~+\text{ }{{8}^{2}}~\ldots \text{ }\left( ii \right) \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

                                                        

    \[\]

Compare (i) and (ii)

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> B{{C}^{2}}~+\text{ }{{8}^{2}}~=\text{ }{{8}^{2}}~+\text{ }{{6}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow B{{C}^{2}}~+\text{ }{{6}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow BC\text{ }=\text{ }6\text{ }m \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

    \[\]

Therefore, the tip of the ladder reaches to a height od

    \[6m.\]

i

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