Asked by Hannah Shleyfer
Given: KLMN is a trapezoid, KL = MN, LM:KN = 1:5
AB
is a midsegment, AB = 18, KL = 15
Find: The height of KLMN
AB
is a midsegment, AB = 18, KL = 15
Find: The height of KLMN
Answers
Answered by
oobleck
Since KL=MN, MN=15
Since AB=18, it must be the midsegment parallel to LM and KN
Thus, LM+KN=36
SO, if LM=x and MN=5x, LM=6 and MN=30
Therefore, if you drop altitudes LC and MD to the base KM,
KC=DN=12
Now you have right triangle KCL with sides 12 and 9, and hypotenuse 15
Thus, the height LC = 9
Since AB=18, it must be the midsegment parallel to LM and KN
Thus, LM+KN=36
SO, if LM=x and MN=5x, LM=6 and MN=30
Therefore, if you drop altitudes LC and MD to the base KM,
KC=DN=12
Now you have right triangle KCL with sides 12 and 9, and hypotenuse 15
Thus, the height LC = 9