Multiple choice

Calculate the length of the hypotenuse of a right-angled triangle if one leg is $3$ inches longer than the other one and the area of the triangle is $35$ square inches.

  1. $10$
  2. $\displaystyle\frac{\sqrt{35}}{2}$
  3. $7\sqrt{10}$
  4. $\sqrt{149}$
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D Correct answer
Explanation

Let the legs be x and x+3. Area = 0.5 * x * (x+3) = 35, so x^2 + 3x - 70 = 0. Solving gives x = 7 or -10. The legs are 7 and 10. The hypotenuse is sqrt(7^2 + 10^2) = sqrt(49 + 100) = sqrt(149).

AI explanation

Let the shorter leg be x, making the longer leg x + 3. The area of a right triangle is 1/2 * base * height, so 1/2 * x * (x + 3) = 35, which simplifies to x^2 + 3x - 70 = 0. Solving this quadratic equation yields x = 7, meaning the legs are 7 inches and 10 inches. Using the Pythagorean theorem, the hypotenuse is sqrt(7^2 + 10^2) = sqrt(149) inches.

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