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Question

Find the length of RS if S is between R and T, the length of RS is 1/3 the length RT, RS=3x-3, and ST=2x+6.

Answer 1

RT = RS +ST

ST =2x+6

RT = 5x+3

RS = RT/3 = (5x+3)/3

5x+3 = (5x+3)/3 + 2x+6

15x+9 = 5x+3 +6x +18

15x-11x = 12

4x = 12

x =3

RS = (5(3)+3)/3 = 18/3 = 6

ST =2x+6 = 2(3)+6) = 12

RT = 3RS = 9

Answer 2

Answer 3

RS = 1/3 ( RT) = 3X -3

ST = 2X +3

RT = 3 ( 3X -3) = 9X -9

RT = RS + ST = 9 X -9 = 3X - 3 + 2 X +3 = 5X

9X - 9 = 5X

4X = 9

X = 9/4

Rs= 3X - 3 = 3 (9/4) -3 = 27/3 -4 = (27-12 )/4 = 15/4