Question

Point L is on line segment KM. Given KM = 5x + 10, LM = 4x, and KL = 3x, determine the numerical length of KL.

a) 12
b) 15
c) 18
d) 21

Answer 1

The length of segment KL is determined by setting the equation 5x + 10 = 7x, which simplifies to x = 5. Substituting x back into KL = 3x gives us KL = 15, corresponding to answer choice (b).

Step-by-step explanation:

We are given three segments on the same line: KM, LM, and KL. To find the numerical length of KL, we can use the fact that segment KM is the sum of segments LM and KL. We're given KM = 5x + 10, LM = 4x, and KL = 3x. Setting up the equation, we get:

5x + 10 = 4x + 3x

Now, we combine like terms:

5x + 10 = 7x

Subtracting 5x from both sides gives us:

10 = 2x

Dividing both sides by 2 gives us:

x = 5

Now we can plug this value of x back into the expression for KL:

KL = 3x

KL = 3(5)

KL = 15

So the length of segment KL is 15, which corresponds to answer choice (b).