Question

Find the height of the triangle by applying formulas for the area of a triangle and

Answer 1

Answer:

Step-by-step explanation:

a= 12 mm ; b = 16 mm  ; c = 18 mm

s = (a + b+c)/2

$=\dfrac{12 + 16 + 8}{2}\\\\= \dfrac{36}{2}\\\\= 18$

s -a =  18 -  12 = 6 mm

s  -b = 18 - 16 = 2 mm

s  -c = 18 - 8 = 10 mm

$area = \sqrt{s(s -a)(s-b)(s-c)}$

       $= \sqrt{18*6*2*10}\\\\= \sqrt{2160 }\\\\=46.47\\\\=46 \ mm^{2}$

$\dfrac{1}{2}* \ base * \ height = 46\\\\\dfrac{1}{2}*16* \ height = 46\\\\height = \dfrac{46*2}{16}$

  = 5.75

Height = 5.8 mm

Answer 2

Answer:

A. 5.8mm

Step-by-step explanation:

$area \: of \: triangle = \sqrt{s(s - a) \times (s - b) \times (s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{12 + 8 + 16}{2} \\ s = 18 \\ area \: of \: triangle \: = \sqrt{18(18 - 12) \times (18 - 8) \times (18 - 16)} \\ = \sqrt{2160} \\ = 46.47 {m}^{2} \\ area \: of \: triangle \: = \frac{1}{2} \times base \times height \\ 46.47 = \frac{1}{2} \times 16 \times h \\ h = \frac{46.47}{8} \\ h = 5.8mm$