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In the diagram. Find h
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In the diagram. Find h

In the diagram. Find h

A.

$\frac{12}{7}$ cm

B.

$\frac{12}{7} \sqrt{6}$ cm

C.

$\frac{7}{12}$ cm

D.

$\frac{1}{2}$ cm

View answer & explanation

Correct answer is B

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 = $\frac{12}{h} \sqrt{6}$

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