From the figure we have ABCD is a parallelogram with base AB = 20 cm and corresponding altitude DL.
It is given that the area of the parallelogram ABCD = 100 cm2
We know that the area of a parallelogram = Base x Height
Therefore,
100 = AB x DL
100 = 20 x DL
DL = 100/20 = 5 cm
By observing the picture it is clear that we have to apply the Pythagoras theorem,
Therefore by Pythagoras theorem, we have,
(AD)2= (AL)2 + (DL)2
(13)2 = (AL)2+ (5)2
(AL)2 = (13)2 – (5)2
(AL)2 = 169 – 25
= 144
We know that 122= 44
(AL)2 = (12)2
AL = 12 cm
Hence, length of AL is 12 cm.
