Question

In a parallelogram ABCD, AB =18cm, BC=12cm, AL perpendicular to DC and AM perpendicular to BC.
If AL=6.4 cm, find the length of AM​

Answer 1

Step-by-step explanation:

This can be done with concept of similarity of triangles.

ABCD is a parallelogram

So angle B=Angle D

Also BC=AD= 12cm

In ΔADL and ΔABM

angle D= Angle B (proved)

angle ALD = angle AMB (each 90 degrees)

Therefore Δ ADL similar to Δ ABM

AL/AM = AD/AB

AD/AB=12/18=2/3

Therefore AL/AM=2/3

AL= 6.4cm

Therfore AM=9.6cm

length of AM =9.6cm