In the given figure, AB $= 12$ cm, AC $= 13$ cm, CE $= 10$ cm and DE $= 6$ cm. Calculate the length of BD.

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Solution

Given $A B = 12 c m, A C = 13 c m, C E = 10 c m a n d D E = 6 c m$
$A B C$ is a right triangle.
$A C^{2} = A B^{2} + B C^{2}$ [Pythagoras theorem]
$13^{2} = 12^{2} + B C^{2}$
$B C^{2} = 13^{2} - 12^{2}$
$B C^{2} = 169 - 144$
$B C^{2} = 25$
Taking square root on both sides,
$B C = 5 c m$
$C D E$ is a right triangle.
$C E^{2} = C D^{2} + D E^{2}$ [Pythagoras theorem]
$10^{2} = C D^{2} + 62$
$100 = C D^{2} + 36$
$C D^{2} = 100 - 36$
$C D^{2} = 64$
Taking square root on both sides,
$C D = 8 c m$
$B D = B C + C D$
$B D = 5 + 8$
$B D = 13 c m$
Hence the length of $B D$ is $13 c m .$

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In the given figure, AB=12cm, AC=13cm, CE=10cm and DE=6cm. Calculate the length of BD.

In the given figure, AB $= 12$ cm, AC $= 13$ cm, CE $= 10$ cm and DE $= 6$ cm. Calculate the length of BD.