35.5k views
5 votes
RS = 2x, ST = 5x + 4, and RT = 32. What is the value of RS & X?

a) RS = 8, X = 4
b) RS = 12, X = 6
c) RS = 16, X = 8
d) RS = 20, X = 10

User Christeen
by
7.8k points

1 Answer

0 votes

Final answer:

The length of segment RS is 8 units, and the value of x is 4. We found this by setting up an equation combining RS and ST to equal the total length RT, then solving for x to find the specific length of RS.

Step-by-step explanation:

The student is trying to find the length of the segment RS and the value of x given that RS = 2x, ST = 5x + 4, and RT = 32. We are given four options to choose from. We can solve this by setting up an equation since RS + ST = RT.

First, let's write down the equation by substituting the given expressions for RS and ST:

2x (RS) + (5x + 4) (ST) = 32 (RT)

Now let's solve for x:

2x + 5x + 4 = 32 ⇒ 7x + 4 = 32 ⇒ 7x = 28 ⇒ x = 4

Now that we have the value of x, we can find RS:

RS = 2x = 2(4) = 8

Therefore, the value of RS is 8 and x is 4, which corresponds to option (a).

User Dendi Suhubdy
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.