Question

Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.This is a triangle. side a has a length of 9mm. side b has a length of 6 mm. side c has a length of 12 mm. The altitude to side c has a length of X mm.A. 4.3 mmB. 2.2 mmC. 6.2 mmD. 5.8 mm

Answer 1

Given

To find the height of the triangle.

Step-by-step explanation:

It is given that,

Consider the area of the triangle as,

`\begin{gathered} A=√(s(s-a)(s-b)(s-c)) \\ Where\text{ }s=(a+b+c)/(2) \\ s=(9+6+12)/(2) \\ s=(27)/(2) \\ s=13.5 \end{gathered}`

That implies,

`\begin{gathered} A=√(13.5(13.5-9)(13.5-6)(13.5-12)) \\ =√(13.5*4.5*7.5*1.5) \\ =√(683.4375) \\ =26.1426mm^2 \end{gathered}`

Since area of the triangle can be written as,

`\begin{gathered} A=(1)/(2)* b* h \\ 26.1426=(1)/(2)*12* X \\ 26.1426=6X \\ X=(26.1426)/(6) \\ X=4.3mm \end{gathered}`

Hence, the answer is 4.3 mm.