if BE=50m then length of AD is

50m

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60m

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40m

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70m

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Solution

The correct option is B 60m
$G i v e n - A B E i s a r i g h t t r i a n g l e w i t h A B a s h y p o t e n u s e a n d ∠ A B E = 45^{o}, B E = 50 m . B C D E i s a r e c t a n g l e . T o f i n d o u t - A D = ? S o l u t i o n - A B E i s a r i g h t t r i a n g l e w i t h A B a s h y p o t e n u s e . ∴ ∠ A E B = 90^{o} . A g a i n B C D E i s a r e c t a n g l e . ∴ ∠ D E B = 90^{o} . S o ∠ A E B + ∠ D E B = 90^{o} + 90^{o} = 180^{o} . ∴ ∠ A E B & ∠ D E B a r e l i n e a r p a i r . i . e A E D i s a s t r a i g h t l i n e . N o w \frac{A E}{B E} = tan 45^{o} = 1. ∴ A E = B E = 50 m . A l s o D E = B C = 10 m . ∴ A D = A E + D E = 50 m + 10 m = 60 m . A n s - O p t i o n B .$

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