Question

Point A is in between line segment Lˣ, and points A, L, and X are collinear. Line segment LA has a length of (x + 2), and line segment AX has a length of (2x + 4). If line segment Lˣ has a length of 48, then determine the length of segments LA and AX.

Answer 1

To find the lengths of segments LA and AX, we can set up an equation using the given information and solve it. The length of LA is 16 units and the length of AX is 32 units.

Step-by-step explanation:

To solve this problem, we can set up an equation using the given information.

Let's call the length of LA as a and the length of AX as b. We know that the length of Lˣ is 48.

From the problem, we can write the equation: a + b = 48

We also know that the length of LA is (x + 2) and the length of AX is (2x + 4).

Substituting these values into the equation, we get: (x + 2) + (2x + 4) = 48

Simplifying the equation, we have: 3x + 6 = 48

Subtracting 6 from both sides, we get: 3x = 42

Dividing both sides by 3, we find that x = 14.

Finally, substituting the value of x into the expressions for a and b, we get:

LA = x + 2 = 14 + 2 = 16

AX = 2x + 4 = 2(14) + 4 = 32.