![\[\mathbf{6}\text{ }\mathbf{m}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0a07f6483f265e6e47c316121ac8cca7_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{8}\text{ }\mathbf{m}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f5dd6c4c521acc9e7e7137b3036d18fb_l3.png "Rendered by QuickLaTeX.com")
Solution:
Let’s assume the length of ladder to be, AD = BE = x m
So, in ∆ACD, by Pythagoras theorem
We have,
![\[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> A{{D}^{2}}~=\text{ }A{{C}^{2}}~+\text{ }C{{D}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow {{x}^{2}}~=\text{ }{{8}^{2}}~+\text{ }{{6}^{2}}~\ldots \text{ }\left( i \right) \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-310bd597a7ba8cb598d0b2427732e745_l3.png "Rendered by QuickLaTeX.com")
![\[\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1833cc7760eba792ec467db2c623cfe8_l3.png "Rendered by QuickLaTeX.com")
Also, in ∆BCE, by Pythagoras theorem
![\[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> B{{E}^{2}}~=\text{ }B{{C}^{2}}~+\text{ }C{{E}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow {{x}^{2}}~=\text{ }B{{C}^{2}}~+\text{ }{{8}^{2}}~\ldots \text{ }\left( ii \right) \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-04003e772ad3fd11af4831b8b3d4080b_l3.png "Rendered by QuickLaTeX.com")
Compare (i) and (ii)
![\[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> B{{C}^{2}}~+\text{ }{{8}^{2}}~=\text{ }{{8}^{2}}~+\text{ }{{6}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow B{{C}^{2}}~+\text{ }{{6}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow BC\text{ }=\text{ }6\text{ }m \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bfbf8fd1637542a82efe00c2bf06d64d_l3.png "Rendered by QuickLaTeX.com")
Therefore, the tip of the ladder reaches to a height od
![\[6m.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9484ad6d3c28cfa8fdd64a9c68ec62e4_l3.png "Rendered by QuickLaTeX.com")
