ABCD is a rectangle such that AD=2AB and its center is O. H is the top of a pyramid which has ABCD as base. All lateral faces are isosceles triangles. planes (HAB) and (HCD) are ⊥. i have joined a graphic. 1. show that (OH)⊥(ABC). 2. show that OH=((√3)/2)AB


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Question Number 139419 by mathocean1 last updated on 26/Apr/21

$A B C D i s a r e c t a n g l e s u c h t h a t$ $A D = 2 A B a n d i t s c e n t e r i s O .$ $H i s t h e t o p o f a p y r a m i d w h i c h$ $h a s A B C D a s b a s e . A l l l a t e r a l$ $f a c e s a r e i s o s c e l e s t r i a n g l e s . p l a n e s$ $(H A B) a n d (H C D) a r e ⊥ .$ $i h a v e j o i n e d a g r a p h i c .$ $1 . s h o w t h a t (O H) ⊥ (A B C) .$ $2 . s h o w t h a t O H = \frac{\sqrt{3}}{2} A B$
Commented by mathocean1 last updated on 26/Apr/21

Commented by mr W last updated on 26/Apr/21

$O H = A B \neq \frac{\sqrt{3}}{2} A B$
Commented by mr W last updated on 27/Apr/21

Commented by mr W last updated on 27/Apr/21

Commented by mr W last updated on 27/Apr/21

$H E ⊥ H F$ $O H = \frac{E F}{2} = \frac{A D}{2} = A B$
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