Answer:
the length of the first side of the triangle is [tex]\frac{28}{3}\ in[/tex]
the length of the second side of the triangle is [tex]\frac{37}{3}\ in[/tex]
the length of the third side of the triangle is [tex]\frac{19}{3}\ in[/tex]
Step-by-step explanation:
Let
x-----> the length of the first side of a triangle
y----> the length of the second side of a triangle
z---> the length of the third side of a triangle
we know that
[tex]x=y-3[/tex]
[tex]y=x+3[/tex] -----> equation A
[tex]x=z+3[/tex]
[tex]z=x-3[/tex] -----> equation B
The perimeter of the triangle is equal to
[tex]P=x+y+z[/tex]
[tex]P=28\ in[/tex]
so
[tex]28=x+y+z[/tex] -----> equation C
substitute equation A and equation B in equation C
[tex]28=x+(x+3)+(x-3)[/tex]
solve for x
[tex]28=3x[/tex]
[tex]x=\frac{28}{3}\ in[/tex]
Find the value of each side
the first side of a triangle is x
[tex]x=\frac{28}{3}\ in[/tex]
the second side of a triangle is y
[tex]y=\frac{28}{3}+3=\frac{37}{3}\ in[/tex]
the third side of a triangle is z
[tex]z=\frac{28}{3}-3=\frac{19}{3}\ in[/tex]
