In a $Δ A B C, A B = A C = 2.5 c m, B C = 4 c m$ . Find its height from $A$ to the opposite base.

1.5 c m

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1 c m

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2 c m

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3 c m

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Solution

The correct option is A $1.5 c m$
$I n △ A B C$

In order to find height we need to consider that $A D ⊥ B C$

$H e n c e i n r i g h t a n g l e d △ A D C$

${A C}^{2} = {A D}^{2} + {D C}^{2} (P h y t h a g o r e a s T h e o r m)$

$\Rightarrow {A D}^{2} = {A C}^{2} - {D C}^{2}$

$\Rightarrow {A D}^{2} = {(2.5)}^{2} - ({2)}^{2}$

$\Rightarrow {A D}^{2} = 6.25 - 4$

$\Rightarrow {A D}^{2} = 2.25$

$\Rightarrow A D = 1.5$

$H e n c e o p t i o n (A) i s r i g h t a n s w e r$

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