Question

RS = 5y + 2, ST = 2y +9, and RT = 67. Find rs and st

A. rs = 22, st = 31
B. rs = 15, st = 38
C. rs = 25, st = 42
D. rs = 20, st = 29

Answer 1

To solve the problem, we combine the given segment equations and the total length to find the value of 'y' and then substitute back into the segment equations to find the lengths of RS and ST which are 25 and 42 respectively.

Step-by-step explanation:

The student is asking to solve for the lengths of segments RS and ST given the equations RS = 5y + 2, ST = 2y + 9, and the total length RT = 67. To find the values of RS and ST, we first need to combine the equations for RS and ST to set up an equation equal to RT.

RS + ST = RT

(5y + 2) + (2y + 9) = 67

7y + 11 = 67

7y = 56

y = 8

Now that we have the value of y, we can substitute it back into the equations for RS and ST:

RS = 5(8) + 2 = 40 + 2 = 42

ST = 2(8) + 9 = 16 + 9 = 25

This means that RS is 42 and ST is 25, therefore the correct answer is C: RS = 25, ST = 42.