MediumGeometry
How do you find a parallelogram's perimeter when an angle bisector splits a side into 10 cm and 6 cm?
TL;DR
The perimeter of parallelogram KMNR is 52 cm.
Question
In parallelogram KMNR, the bisector of angle MKR meets side MN at E. Find the perimeter if ME = 10 cm and EN = 6 cm.
Answer
The perimeter is 52 cm.
Explanation
Let KE be the bisector. Since ME ∥ KR, angles KEM and EKR are equal. The bisector gives ∠MKE = ∠EKR, so ∠MKE = ∠KEM. Triangle KME is therefore isosceles, with KM = ME = 10 cm.
The other side is MN = ME + EN = 10 + 6 = 16 cm.
The perimeter is P = 2(KM + MN) = 2(10 + 16) = 52 cm.
