Question

The midsegment of ABC IS IM. What is the length of MC if BC is 18 inches
long?

A. 36 inches

B. 18 inches

C.27 inches

D. 9 inches

Answer 1

Answer:

D. 9 inches

Step-by-step explanation:

By using proportionality theorem,

Triangle BLM ~ Triangle BAC

$\frac{bm}{bc} = \frac{bl}{ba}$

as ba = bl + la and as bl = la

Therefore, bl + la = 2bl

$\frac{bm}{bc} = \frac{bl}{2bl}$

Now, we get,

$\frac{bm}{18} = \frac{1}{2}$

as bc = 18

Hence,

$bm = 9 \: inches$

Answer 2

Answer: D. 9 inches

Step-by-step explanation:

Given : The midsegment of Δ ABC is line segment IM.

Such that for side BC ,  BM=MC         [ Show in the picture ]     (1)

and BC= BM+MC    (2)

The length of BC = 18 inches              (3)

From (1) and (2), we have

$BC=MC+MC\\\\\Rightarrow\ BC=2MC$

Using (3), we have

$2MC=18\text{ inches}\\\\\Rightarrow\ MC=\dfrac{18}{2}=9\text{ inches}$

Therefore, the length of MC = 9 inches.

Hence, D is the correct option.