In the diagram Find h - JAMB Mathematics 1994 Question

A_{(\bigtriangleup)} = (\sqrt{S(S - a) (S - b)(S - c)}) (Hero's Formula)

S = (\frac{a + b + c}{2}) = (\frac{5 + 6 + 7}{2})

(\frac{18}{2} = 9)

A_{(\bigtriangleup)} (\sqrt{9} \times 4 \times 3 \times 2)

(\sqrt{216} = 6 \sqrt{6}cm^3)

A_{(\bigtriangleup)} = (\frac{1}{2} \times 6 \times h)

6(\sqrt{6} = \frac{1}{2} \times 7 \times h)

h = (\frac{12}{h} \sqrt{6})