The length of line segment LJ is equal to 15 units.
From the figure,
Angle JKL is a right angle.
An altitude is drawn from point K to point M on side LJ to form a right angle.
The length of KM is 6.
The length of MJ is 3.
We have to find the length of LJ.
Using Pythagoras theorem,
What is the Pythagoras theorem,?
(JK)^2=(MJ)^2+(KM)^2
(JK)^2=(3)^2+(6)^2
(JK)^2=9+36
(JK)^2=45
Taking square root,
JK = √45
JK = √9(5)
JK = 3√5
Let angle KJM be x.
cos x = JM/JK = JK/JL
Substituting the values,
3/3√5 = 3√5/JL
By cross multiplication,
JL = (3√5 × 3√5)/ 3
JL = 9(5) / 3
JL = 3(5)
JL = 15 units
Therefore, JL = LJ = 15 units.
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