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The lengths of the adjacent sides of a right - angled triang...

The lengths of the adjacent sides of a right - angled triangle are xcm, (x-1)cm. If the length of the hypotenuse is $\sqrt{13}cm$ , find the value of x

A.

2

B.

3

C.

4

D.

5

View answer & explanation

Correct answer is B

$x^2+(x-1)^2 = (\sqrt{13})^2 \Rightarrow x^2 + x^2 - 2x + 1 = 13\\ 2x^2 - 2x - 12 = 0$ dividing through by 2
$x^2 - x- 6 = 0; (x-3)(x-2) = 0 \Rightarrow x = 3 or -2$

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