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In the figure below, find the value of 'x'.

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

⇒ (x)^{2} = (7)^{2} + (24)^{2}

⇒ x^{2} = 49 + 576

⇒ x^{2} = 625

⇒ x^{2} = (25)^{2}

⇒ x = 25

∴ The value of x is 25.

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