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In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.

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#### Solution

In the right-angled triangle LMN, ∠M = 90°. Hence, side LN is the hypotenuse.

According to Pythagoras' theorem,

l(LN)^{2} = l(MN)^{2} + l(LM)^{2}

⇒ (20)^{2} = l(MN)^{2} + (12)^{2}

⇒ 400 = l(MN)^{2} + 144

⇒ l(MN)^{2} = 400 − 144

⇒ l(MN)^{2} = 256

⇒ l(MN)^{2} = (16)^{2}

⇒ l(MN) = 16

∴ Length of seg MN = 16 cm.

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