Answer:
y = 4
RS = 35
ST = 26
Step-by-step explanation:
Given:
RS = 8y + 3
ST = 5y + 6
RT = 61
Required:
a. Value of y
b. Numerical lenght of RS and ST
SOLUTION:
a. Points R, S and T are collinear, therefore, based on segment addition postulate, the following equation can be created to find the value of y:
[tex] RS + ST = RT [/tex]
[tex] (8y + 3) + (5y + 6) = 61 [/tex] (substitution)
Solve for y
[tex] 8y + 3 + 5y + 6 = 61 [/tex]
Combine like terms
[tex] 8y + 5y + 3 + 6 = 61 [/tex]
[tex] 13y + 9 = 61 [/tex]
Subtract 9 from both sides
[tex] 13y + 9 - 9 = 61 - 9 [/tex]
[tex] 13y = 52 [/tex]
Divide both sides by 13
[tex] \frac{13y}{13} = \frac{52}{13} [/tex]
[tex] y = 4 [/tex]
b. RS = 8y + 3
Plug in the value of y
RS = 8(4) + 3 = 32 + 3
RS = 35
ST = 5y + 6
Plug in the value of y
ST = 5(4) + 6 = 20 + 6
ST = 26
