PLEASE HELP ME IN THIS

Question

Find the area of LKJ.

1. A.
2. 108 square units
3. 
   
4. B.
5. 300 square units
6. 
   
7. C.
8. 165 square units
9. 
   
10. D.
11. 150 square units

.

Answer 1

I find the easiest way for me is to redraw the 3 triangles that are formed in this way side-by-side in the same orientation like this:

By doing that, it is easy for me to set up a similarity proportion.

In this case, we can see that using the medium size triangle and the small triangle we can say:

KM/LM = JM/KM or plugging in numbers:

12/x = 16/12 and cross multiplying:

12•12 = 16x

144 = 16x

x = 144/16

x = 9

So LM = 9

Once you know that LM = 9, you can add that to JM to get the length of the base JL. So JL = 9 + 16 = 25

Meaning the are of ΔLKJ = 1/2bh = 1/2(25)(12) = 150 square units