Multiple choice

Let ABC be a right-angled triangle with sides 5 cm, 12 cm and 13 cm. If p is the length of the perpendicular drawn from vertex A on the hypotenuse BC, then what is the value of 13p?

  1. 24

  2. 48

  3. 60

  4. 90
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a right triangle, the area is (1/2) * base * height. Area = (1/2) * 5 * 12 = 30. Also, area = (1/2) * hypotenuse * altitude(p) = (1/2) * 13 * p. So 30 = 6.5 * p, which means 13 * p = 60.

AI explanation

The area of a right-angled triangle can be expressed as half the product of its legs or half the product of its hypotenuse and the altitude to the hypotenuse. Equating these two expressions gives 1/2 * 5 * 12 = 1/2 * 13 * p. Solving for p yields p = 60 / 13, so multiplying by 13 gives 13p = 60. The result is 60.

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