Question

Find the value of the variable and LN if M is between L and N. (LM = 2a), (MN = 4a), (LM = 50).

A. (a = 10), (LN = 60)
B. (a = 25), (LN = 100)
C. (a = 12.5), (LN = 62.5)
D. (a = 5), (LN = 60)

Answer 1

The variable a equals 25, and the length of LN is 150. The correct answer was not provided in the options, as the length calculation results in a value not listed.

Step-by-step explanation:

To find the value of the variable a and the length of LN, we need to use the given information. We have LM = 2a, which is given as 50, so we can write:

2a = 50

We divide both sides by 2 to find the value of a:

a = 25

Next, we find the length of MN using the value of a:

MN = 4a = 4(25) = 100

Since M is between L and N, LN = LM + MN, which means:

LN = 50 + 100 = 150

The correct value for a should be 25 and LN should be 150.