Multiple choice

The altitude of a right triangle is $7$ cm less than its base. If the hypotenuse is $13$ cm, find the other two sides.

  1. $4, 7$
  2. $5, 12$
  3. $3, 10$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let base be b, altitude be b-7. Hypotenuse is 13. b^2 + (b-7)^2 = 13^2. b^2 + b^2 - 14b + 49 = 169. 2b^2 - 14b - 120 = 0. b^2 - 7b - 60 = 0. (b-12)(b+5) = 0. Base = 12, altitude = 5.

AI explanation

Let the base of the right triangle be x cm, so the altitude is x minus 7 cm. By the Pythagorean theorem, the sum of the squares of the base and altitude equals the square of the hypotenuse, giving x squared plus (x minus 7) squared equals 13 squared. Expanding this gives x squared plus x squared minus 14x plus 49 equals 169, which simplifies to 2x squared minus 14x minus 120 equals 0. Dividing by 2 yields x squared minus 7x minus 60 equals 0, which factors into (x minus 12)(x plus 5) equals 0. Since the side length must be positive, the base x is 12 cm and the altitude is 5 cm.

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