Multiple choice

The hypotenuse of right triangles is 5 m. If difference between length of other sides is 1 m. Find smallest side.

  1. $3$
  2. $-3$
  3. $4$
  4. $-4$
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A Correct answer
Explanation

Let the sides be x and x+1. By the Pythagorean theorem, x^2 + (x+1)^2 = 5^2. This simplifies to 2x^2 + 2x - 24 = 0, or x^2 + x - 12 = 0. Factoring gives (x+4)(x-3) = 0, so x = 3.

AI explanation

Let the smallest side be x meters, so the other side is x + 1 meters. By the Pythagorean theorem, x squared plus (x + 1) squared equals 5 squared, which simplifies to 2x squared + 2x + 1 = 25. Solving the quadratic equation 2x squared + 2x - 24 = 0 gives x = 3 or x = -4. Since length must be positive, the smallest side is 3.

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