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In the given right-angled triangle ABC, ∠B = 90°. Find the value of x.

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answer is D.

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Detailed Solution

In $Δ A B C, ∠ B = 90 °$

$A B^{2} + B C^{2} = A C^{2}$ (By Pythagoras property)

$5^{2} + {(x - 3)}^{2} = {(x + 2)}^{2}$

$25 + x^{2} + 9 - 6 x = x^{2} + 4 + 4 x$

$- 6 x - 4 x = 4 - 9 - 25$

$- 10 x = - 30$

$x = 3$

Hence, the required value of $x = 3$

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