Answer:
[tex]y = 6[/tex]
[tex]RS = 38[/tex]
[tex]ST = 39[/tex]
[tex]RT = 77[/tex]
Step-by-step explanation:
Given:
[tex]RS = 6y +2[/tex]
[tex]ST=5y + 9[/tex]
[tex]RT= 13y - 1[/tex]
Solving (a): The value of y
From the given parameters, we understand that
[tex]RT = RS + ST[/tex]
Substitute values for RS, ST and RT
[tex]13y - 1 = 6y + 2 + 5y + 9[/tex]
Collect Like Terms
[tex]13y - 6y - 5y = 1 + 2 + 9[/tex]
[tex]2y = 12[/tex]
Divide both sides by 2
[tex]y = \frac{12}{2}[/tex]
[tex]y = 6[/tex]
Solving (b):
The value of RS
Substitute 6 for y in [tex]RS = 6y +2[/tex]
[tex]RS = 6 * 6 + 2[/tex]
[tex]RS = 36 + 2[/tex]
[tex]RS = 38[/tex]
The value of ST
Substitute 6 for y in [tex]ST=5y + 9[/tex]
[tex]ST = 5 * 6 + 9[/tex]
[tex]ST = 30 + 9[/tex]
[tex]ST = 39[/tex]
The value of ST
Substitute 6 for y in [tex]RT= 13y - 1[/tex]
[tex]RT = 13 * 6 - 1[/tex]
[tex]RT = 78 - 1[/tex]
[tex]RT = 77[/tex]
