Question

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

Answer 1

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).