Question

In Fig. 21, if AB = 35 cm, AD = 20 cm and area of the parallelogram is 560 cm², find LB.

Answer 1

We have,
ABCD is a parallelogram with base AB = 35 cm and corresponding altitude DL. The adjacent side of the parallelogram AD = 20 cm.
It is given that the area of the parallelogram ABCD = 560 cm²
Now,
Area of the parallelogram = Base x Height
560 cm² = AB x DL
560 cm² = 35 cm x DL

∴ DL = $\frac{560{\mathrm{cm}}^2}{35\mathrm{cm}}=16\mathrm{cm}$
Again by Pythagoras theorem, we have,
(AD)² = (AL)² + (DL)²
⇒ (20)² = (AL)² + (16)²
⇒ (AL)² = (20)² − (16)²
= 400 − 256 = 144
⇒ (AL)² = (12)²
⇒ AL = 12 cm
From the figure,
AB = AL + LB
35 cm = 12 cm + LB
∴ LB = 35 cm − 12 cm
= 23 cm
Hence, length of LB is 23 cm.