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The lengths of the adjacent sides of the right angle of a right-angled triangle are (x - 2) cm and 22x2\sqrt{2}x cm. If the length of the hypotenuse is 3 cm, then the value of x is :

  1. 1

  2. 2

  3. 3

  4. 4

Pythagoras Theorem

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Answer

The lengths of the adjacent sides of the right angle of a right-angled triangle. Pythagoras Theorem, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

In right triangle ABC,

By pythagoras theorem we get,

Hypotenuse2 = Base2 + Height2

⇒ AC2 = BC2 + AB2

⇒ 32 = (x - 2)2 + (22x)2(2\sqrt{2}\text{x})^2

⇒ 9 = x2 + 4 - 4x + 4 × 2 x2

⇒ 9 = x2 + 4 - 4x + 8x2

⇒ 9x2 - 4x + 4 - 9 = 0

⇒ 9x2 - 4x - 5 = 0

⇒ 9x2 - 9x + 5x - 5 = 0

⇒ 9x(x - 1) + 5(x - 1) = 0

⇒ (9x + 5) = 0 or (x - 1) = 0

⇒ x = - 59\dfrac{5}{9} or x = 1

Since, length cannot be negative.

⇒ x = 1 cm.

Hence, option 1 is the correct option.

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