What is the length of line segment LJ?
9 units, 12 units, 15 units, 18 units
Solution:
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,
\((JK)^{2}=(MJ)^{2}+(KM)^{2}\)
\((JK)^{2}=(3)^{2}+(6)^{2}\)
\((JK)^{2}=9+36\)
\((JK)^{2}=45\)
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
JL = (3√5 × 3√5)/ 3
JL = 9(5) / 3
JL = 3(5)
JL = 15 units
Therefore, JL = LJ = 15 units.
What is the length of line segment LJ?
Summary:
The length of the line segment LJ is 15 units.