If the sides of a right angled triangle are $x, 3 x + 3$ and $3 x + 4$ , then $x$ is equal to:

- 1

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7

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6

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Both A and B

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Solution

The correct option is A $7$
As the sides are of a right angled triangle, we have
${H y p o t e n u s e}^{2} = {S i d e 1}^{2} + {S i d e 2}^{2}$ where hypotenuse is the largest side.
${(3 x + 4)}^{2} = {(3 x + 3)}^{2} + x^{2}$
$=> 9 x^{2} + 16 + 24 x = 9 x^{2} + 9 + 18 x + x^{2}$
$=> x^{2} - 6 x - 7 = 0$
$=> x^{2} - 7 x + x - 7 = 0$
$=> x (x - 7) + (x - 7) = 0$
$=> (x - 7) (x + 1) = 0$
$=> x = 7, - 1$
As the side cannot be negative, $x = 7$ .

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