Multiple choice

If the hypotenuse of a right angled triangle is 6 cm longer than the shortest leg and the longer leg is 3 cm more than the shortest leg, find the length of the shortest leg.

  1. 14 cm

  2. 12 cm

  3. 10 cm

  4. 9 cm
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D Correct answer
Explanation

Let the shortest leg be x. Hypotenuse = x + 6, longer leg = x + 3. By Pythagoras: x^2 + (x + 3)^2 = (x + 6)^2. Solving x^2 + x^2 + 6x + 9 = x^2 + 12x + 36 gives x^2 - 6x - 27 = 0. Factoring (x - 9)(x + 3) = 0, so x = 9.

AI explanation

Let the shortest leg be x, so the longer leg is x + 3 and the hypotenuse is x + 6. Using the Pythagorean theorem, x^2 + (x+3)^2 = (x+6)^2, which simplifies to x^2 - 6x - 27 = 0. Factoring gives (x-9)(x+3) = 0, meaning x = 9, so the shortest leg is 9 cm.

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