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ABC is a triangle, right angled at A. The resultant of the forces acting along AB, BC with magnitudes (1)/(AB) and (1)/(AC) respectively is the force along AD, where D is the foot of the perpendicular from A on to BC. The magnitude of the resultant is

1. (AB²+AC²)/((AB)²(AC)²)
2. ((AB)(AC))/(AB+AC)
3. (1)/(AB)+(1)/(AC)
4. (1)/(AD)

Correct answer: (1)/(AD)

Solution

Forces 1/AB and 1/AC act along the perpendicular sides AB and AC, so the resultant magnitude is sqrt((1/AB)^2 + (1/AC)^2). Since AD is the altitude to the hypotenuse, 1/AD^2 = 1/AB^2 + 1/AC^2, hence the magnitude equals 1/AD.

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