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Basics of Geometry

In ABC, if ...

Question

In $△ A B C$ , if $∠ B = 90^{o}$ , $A C = 5 c m$ , and $A B = 3 c m$ what is the length of $B C$ ?

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Solution

In $△ A B C, ∠ A B C = 90^{o}$ ....... $(i)$ [Given]
$A C = 5 c m, A B = 3 c m$ ........ [Given]
From $(i)$
${A C}^{2} = {A B}^{2} + {B C}^{2}$ ....... (By Pythagoras theorem)
$⟹ {B C}^{2} = {A C}^{2} - {A B}^{2}$
$⟹ B C^{2} = 5^{2} - 3^{2} = 25 - 9 = 16$
$∴ B C = \sqrt{16} = 4 c m$

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