Option b: 10 in, 18.5 in, 31.5 in.
Explanation:
The three sides of a triangle are [tex]2y+1, 3y+5[/tex] and [tex]7y[/tex]
The perimeter of the triangle is [tex]60 in[/tex].
Since, Perimeter = all sides of the triangle
Let us add all the three sides to determine the length of each side.
[tex]Perimeter=2y+1+3y+5+7y[/tex]
Substituting the value of Perimeter and simplifying, we get,
[tex]60=12y+6\\54=12y\\4.5=y[/tex]
Substituting [tex]y=4.5[/tex] in the three sides of the triangle [tex]2y+1, 3y+5[/tex] and [tex]7y[/tex], we get,
[tex]2y+1=2(4.5)+1=10 in[/tex]
[tex]3y+5=3(4.5)+5=18.5 in[/tex]
[tex]7y=7(4.5)=31.5 in[/tex]
Thus, the lengths of each side are 10 in, 18.5 in, 31.5 in.
