Question

Let S be between R and T. Use the Segment Addition Postulate to solve for m.

RS= 2m + 2, ST= 3m + 3, and RT= 15

A. m= 3

B. m= 2

C. m= 9

D. m= 4

Answer 1

To solve for m using the Segment Addition Postulate, one must combine the expressions for RS and ST, set the sum equal to RT, and solve the resulting equation. The solution for m in this case is 2.

Step-by-step explanation:

The question asks us to use the Segment Addition Postulate to solve for m. The Segment Addition Postulate states that if point S is between R and T, then RS + ST = RT. We are given the lengths of RS, ST, and RT in terms of m, and we need to find the value of m.

First, we write down the equation given by the Segment Addition Postulate:

RS + ST = RT

Then we substitute the given expressions for RS, ST, and RT:

(2m + 2) + (3m + 3) = 15

We combine like terms:

5m + 5 = 15

Next, we subtract 5 from both sides of the equation:

5m = 10

Lastly, we divide both sides by 5 to solve for m:

m = 2

The correct answer is B. m = 2.