# 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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