A Right Angle Triangle Has Hypotenuse Of Length P Cm And One Side Of Length P Cm. If Q−p=2 Express The Length Of Third Side Of Right Angle Triangle In Terms Of Q.

Let x be the third side of the right angle triangle.

Therefore,

\( q^{2} = p^{2} + x^{2} \) \( \Rightarrow x^{2} = q^{2} – p^{2} \) \( \Rightarrow (q – p) (q + p) \)

Since q – p = 2

\( \Rightarrow 2(q + p) \) \( \Rightarrow 2(q + (q-2)) \) \( \Rightarrow 4(q-1) \) \( \Rightarrow x = \sqrt{4 (q – 1)} \) \( \Rightarrow 2\sqrt{q-1} \)

Hence the length of the third side of the right angle triangle in terms of q is \( 2\sqrt{q-1} \)

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