Question

In Fig., ABCD is a parallelogram, DL ⊥ AB. If AB = 20 cm, AD = 13 cm and area of the parallelogram is 100 cm², find AL.

Answer 1

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.