Find the lower height of the triangle ABC if AB = 5cm BC = 7cm and AC = 6cm.

Using Heron’s formula, we determine the area of the original triangle.

S = √ (p * (p – a) (p – b) (p – c)) = √ (9 * (9 – 5) (9 – 7) (9 – 6)) = 6√6.

Knowing that its lower height is drawn to the larger side of the triangle, we define the larger side of this triangle. This is the BC side (7 cm). Then:

S = 0.5 (a * h).

S = 6√6.

0.5 (a * h) = 6√6.

a * h = 12√6.

h = 12√6 / 7.

Answer: h = 12√6 / 7.