Question

A right angled triangle has hypotenuse of length q cm and one side is p cm express the length of third side in terms if q

Answer 1

$\textbf{ By Pythagoras Theorem}$



Hypotenuse² = ( I side )² + ( II side )²



=> ( q )² = ( p )² + ( II side )²


=> q² - p² = ( II side )²


$\mathbf{ \sqrt{ {q}^{2} - {p}^{2} } = II \: side}$







$\mathbf{ Length \: \: of \: \: R emaining \: \: side \: \: is \: \: \sqrt{q^{2}-p^{2}} \: cm}$

Answer 2

Given ∆ is a right angled - triangle,
Hence, By Pythagoras Theorem,



Hypotenuse = q cm
One side = p cm
Second side = ?



Applying Pythagoras Theorem,

Hypotenuse² = base² + height²

q² = p² + height²

q² - p² = height²


$\sqrt{ {q}^{2} - {p}^{2} } = height$




Third side is √[ q²- p² ] cm