What is x?

triangle l m n has a lie segment going from point m to point o, which is on side l n. angles l m o and n m o are equal in measure. line segment m n is twelve centimeters, line segment n o is five centimeters, line segment p l is fourteen centimeters and line segment l m is x centimeters long.

question 3 options:

x equals 35 over 6

x equals 30 over 7

x equals 168 over 5

x equals 196 over 19

Option 3) 24 is right.

Step-by-step explanation:

Given in the picture is a triangle LMN. sides are MN = 12, LN = 21 and LM = x cm

Also MO is the angle bisector of angle M.

By applying angle bisector theorem for triangles we get

LM/MN = LO/NO

i.e. x/12 = 14/7

Simplify to get x = 24

Hence option 3 is right

Verify:

Check whether angle bisector theorem is true.

The proportion LM/MN =24/12 = 2

The proportion LO/NO  =14/7 =2

Both are equal and hence verified

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.