9514 1404 393
Answer:
D. 37.5 square units
Step-by-step explanation:
There are a couple of ways to figure this.
1. The altitude KM is the geometric mean of the segment lengths ML and MJ
KM = √(ML·MJ)
ML = KM²/MJ = 36/8 = 4.5
Then LJ = 4.5 +8 = 12.5, and the area of the triangle is ...
A = (1/2)bh
A = (1/2)(12.5)(6) = 37.5 . . . square units
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2. Triangle LKM is similar to triangle KJM. The scale factor is ...
KM/JM = 6/8 = 3/4
Then the area of triangle LKM is (3/4)² = 9/16 of the area of triangle KJM.
The total area is ...
Area of LJK = (area of KJM)×(1 + 9/16)
= (1/2)(8)(6)(25/16) = 75/2 = 37.5 . . . square units
