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?

Explanation

The area of the right-angled triangle can be calculated in two ways: \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 12 = 30. Using the hypotenuse as the base: \frac{1}{2} \times 13 \times p = 30 \implies 13p = 60.

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