What is the ratio between the base edge, slant height and height of a square pyramid having equal edges?

1:2:2

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$\sqrt{2} : 2 : 3$

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$2 : \sqrt{3} : \sqrt{2}$

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1:1:1

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Solution

The correct option is C
$2 : \sqrt{3} : \sqrt{2}$

Let the equal edge be 2a.

Then, the slant height = $\sqrt{(L a t e r a l e d g e)^{2} - (H a l f t h e b a s e e d g e)^{2}}$

$\Rightarrow$ The slant height = $\sqrt{(2 a)^{2} - (\frac{2 a}{2})^{2}} = \sqrt{3 a^{2}} = \sqrt{3} a$

The height of the pyramid = $\sqrt{(S l a n t h e i g h t)^{2} - (H a l f t h e b a s e e d g e)^{2}}$

$\Rightarrow$ The height of the pyramid $= \sqrt{(\sqrt{3} a)^{2} - (a)^{2}} = \sqrt{2} a$

Thus, the ratio between the base edge, slant height and height of the square pyramid is $2 a : \sqrt{3} a : \sqrt{2} a$

$\Rightarrow$ The ratio = $2 : \sqrt{3} : \sqrt{2}$

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