Answer:
Option C is correct.
[tex]10x+4y+5z =20[/tex]
Step-by-step explanation:
The intercept form of the equation of plane is given by:
[tex]\frac{x}{a}+\frac{y}{b} +\frac{z}{c} = 1[/tex] .....[1]
where
a is the intercept of x-axes
b is the intercept of y-axes and
c is the intercept of z-axes
From the given diagram:
a = 2
b = 5
c = 4
Substitute these in equation [1] we have;
[tex]\frac{x}{2}+\frac{y}{5} +\frac{z}{4} = 1[/tex]
LCM of 2, 5 and 4 is 20
[tex]\frac{10x+4y+5z}{20} = 1[/tex]
Multiply equation 20 both sides we get;
[tex]10x+4y+5z =20[/tex]
Therefore, the equation of plane that contains the given triangle is, [tex]10x+4y+5z =20[/tex]
