Question-88886

Question Number 88886 by I want to learn more last updated on 13/Apr/20

Commented by I want to learn more last updated on 13/Apr/20

ABCD is a square, find AB .

Please help

Commented by I want to learn more last updated on 13/Apr/20

Thanks sir

Commented by john santu last updated on 14/Apr/20

A F i s t h e b i s e c t o r o f t h e a n g l e

D A E

Commented by mr W last updated on 14/Apr/20

x = s i d e l e n g t h o f s q u a r e

α + 2 β = \frac{π}{2} \Rightarrow β = \frac{π}{4} - \frac{α}{2}

\tan α = \frac{36}{x}

\tan β = \frac{64}{x} = \frac{16}{9} \tan α

\frac{1 - \tan \frac{α}{2}}{1 + \tan \frac{α}{2}} = \frac{16}{9} \times \frac{2 \tan \frac{α}{2}}{1 - \tan^{2} \frac{α}{2}}

1 - \tan \frac{α}{2} = \frac{16}{9} \times \frac{2 \tan \frac{α}{2}}{1 - \tan \frac{α}{2}}

1 - 2 \tan \frac{α}{2} + \tan^{2} \frac{α}{2} = \frac{32}{9} \tan \frac{α}{2}

9 - 50 \tan \frac{α}{2} + 9 \tan^{2} \frac{α}{2} = 0

\tan \frac{α}{2} = \frac{25 - 4 \sqrt{34}}{9} \Rightarrow \tan α = \frac{2 \times \frac{25 - 4 \sqrt{34}}{9}}{1 - {(\frac{25 - 4 \sqrt{34}}{9})}^{2}} = \frac{9 \sqrt{34}}{136}

x = \frac{36 \times 136}{9 \sqrt{34}} = 16 \sqrt{34} \approx 93.295

Commented by I want to learn more last updated on 17/Apr/20

Thanks sir

Answered by john santu last updated on 14/Apr/20

A E = 100

t h e n A B = \sqrt{100^{2} - 36^{2}}

= \sqrt{136 \times 64} = 8 \sqrt{136}

= 16 \sqrt{34} \leftarrow t h e a n s w e r

Commented by I want to learn more last updated on 17/Apr/20

How is AE 100 sir

Commented by mr W last updated on 18/Apr/20

Commented by mr W last updated on 18/Apr/20

Δ E A F^{'} i s i s o s c e l e s .

A E = E F^{'} = 36 + 64 = 100

Commented by I want to learn more last updated on 19/Apr/20

I appreciate sir .