Question

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

your knowledge about triangles.

A. 5.8 mm
B. 2.0 mm
OC. 4.4 mm
D. 6.2 mm

Answer 1

A. 5.8mm

Explanation:

`area \: of \: triangle = √(s(s - a) * (s - b) * (s - c)) \\ s = (a + b + c)/(2) \\ s = (12 + 8 + 16)/(2) \\ s = 18 \\ area \: of \: triangle \: = √(18(18 - 12) * (18 - 8) * (18 - 16)) \\ = √(2160) \\ = 46.47 {m}^(2) \\ area \: of \: triangle \: = (1)/(2) * base * height \\ 46.47 = (1)/(2) * 16 * h \\ h = (46.47)/(8) \\ h = 5.8mm`

Answer 2

Explanation:

a= 12 mm ; b = 16 mm ; c = 18 mm

s = (a + b+c)/2

`=(12 + 16 + 8)/(2)\\\\= (36)/(2)\\\\= 18\\\\`

s -a = 18 - 12 = 6 mm

s -b = 18 - 16 = 2 mm

s -c = 18 - 8 = 10 mm

`area = √(s(s -a)(s-b)(s-c))`

`= √(18*6*2*10)\\\\= √(2160 )\\\\=46.47\\\\=46 \ mm^(2)\\`

`(1)/(2)* \ base * \ height = 46\\\\(1)/(2)*16* \ height = 46\\\\height = (46*2)/(16)\\\\`

= 5.75

Height = 5.8 mm