Multiple choice

The hypotenuse of a right triangle is $6$ m more than twice the shortest side. If the third side is $2$ m less than the hypotenuse, find the hypotenuse of the triangle.

  1. $24$ m
  2. $34$ m
  3. $26$ m
  4. $10$ m
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C Correct answer
Explanation

Let the shortest side be x. Hypotenuse = 2x + 6. Third side = (2x + 6) - 2 = 2x + 4. By Pythagoras theorem, x^2 + (2x + 4)^2 = (2x + 6)^2. Solving x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36 gives x^2 - 8x - 20 = 0, so (x-10)(x+2) = 0. Thus x = 10, and the hypotenuse is 2(10) + 6 = 26.

AI explanation

Let the shortest side be x, making the hypotenuse 2x plus 6, and the third side 2x plus 4. By Pythagoras theorem, x squared plus (2x plus 4) squared equals (2x plus 6) squared. Solving 5x squared plus 16x plus 16 equals 4x squared plus 24x plus 36 yields x squared minus 8x minus 20 equals 0, which factors to (x minus 10)(x plus 2) equals 0, meaning x is 10. The hypotenuse is 2(10) plus 6, which is 26 m.

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