Question

Sm, dt, and re are medians. Given SD = 6, TM = 4, and ST = 10, find each value.

a) sm = 12, dt = 20, re = 18
b) sm = 4, dt = 6, re = 10
c) sm = 6, dt = 4, re = 8
d) sm = 18, dt = 12, re = 20

Answer 1

The medians are as follows: sm = 12, dt = 20, re = 18. The correct answer is option a.

Step-by-step explanation:

To find the values of sm, dt, and re, we can use the properties of medians in a triangle. In a triangle, medians divide each other into segments that have a ratio of 2:1. Given that ST = 10, SM = 4, and SD = 6, we can set up the equation:

SM/SD = ST/SM

4/6 = 10/SM

Cross multiplying, we get:

SM * 10 = 4 * 6

Simplifying, we find that SM = 12.

Similarly, we can find dt and re using the same equation. Plugging in the given values, we get:

DT/TM = ST/DT

DT/4 = 10/DT

After cross-multiplying and simplifying, we find that DT = 20.

Finally, we can find re using the equation:

RE/SM = ST/RE

RE/12 = 10/RE

After cross-multiplying and simplifying, we find that RE = 18.

Therefore option a is correct.