Answer:
The perimeter is equal to [tex]67.5\ in[/tex]
Step-by-step explanation:
In this problem we have a ratio of three numbers
[tex]2:3:4[/tex]
Let
x------> the first side (shortest side)
y------> the second side
z------> the third side
we know that
[tex]\frac{x}{y}=\frac{2}{3}[/tex] --> [tex]y=\frac{3}{2}x=1.5x[/tex] ----> equation A
[tex]\frac{x}{z}=\frac{2}{4}[/tex] ---> [tex]z=\frac{4}{2}x=2x[/tex] -----> equation B
[tex]x=15\ in[/tex]
Substitute the value of x in the equation A and equation B
[tex]y=1.5(15)=22.5\ in[/tex]
[tex]z=2(15)=30\ in[/tex]
Find the perimeter of triangle
Remember that the perimeter is equal to the sum of the length sides
[tex]P=x+y+z=15+22.5+30=67.5\ in[/tex]
