Question

Point S is on line segment \overline{RT} RT . Given RT=x+5,RT=x+5, ST=4x-9,ST=4x−9, and RS=x-2,RS=x−2, determine the numerical length of \overline{RT}. RT .

Answer 1

9 units

Explanation:

If point S is on the line RT, then RS + ST = RT

Given

RT=x+5

ST=4x−9

RS=x-2

Substitute into the formula

x-2+4x-9 = x + 5

Collect like terms

x+4x-2-9 = x+5

5x - 11 = x + 5

5x - x = 5+11

4x = 16

x = 4

Get RT

RT = x+5

RT = 4 + 5

RT = 9 units

Hence the length of RT is 9 units