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

D. 9 inches

Explanation:

By using proportionality theorem,

Triangle BLM ~ Triangle BAC

`(bm)/(bc) = (bl)/(ba)`

as ba = bl + la and as bl = la

Therefore, bl + la = 2bl

`(bm)/(bc) = (bl)/(2bl)`

Now, we get,

`(bm)/(18) = (1)/(2)`

as bc = 18

Hence,

`bm = 9 \: inches`

Answer 2

Answer: D. 9 inches

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=(18)/(2)=9\text{ inches}`

Therefore, the length of MC = 9 inches.

Hence, D is the correct option.