In Fig. 21, ABCD is a parallelogram, DL ⊥ AB. If AB = 20 cm, AD = 13 cm and area of the parallelogram is 100 cm², find AL.

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Solution

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
Now,
Area of a parallelogram = Base x Height
100 cm² = AB x DL
100 cm² = 20 cm x DL
∴ DL = $\frac{100 {cm}^{2}}{20 cm} = 5 cm$
Again by Pythagoras theorem, we have,
(AD)² = (AL)²+ (DL)²
⇒ (13)² = (AL)² + (5)²
⇒ (AL)²= (13)²- (5)² = 169 − 25 = 144
⇒ (AL)² = (12)²
⇒ AL = 12 cm
Hence. length of AL is 12 cm.

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In Fig. 21, ABCD is a parallelogram, DL ⊥ AB. If AB = 20 cm, AD = 13 cm and area of the parallelogram is 100 cm2, find AL.

In Fig. 21, ABCD is a parallelogram, DL ⊥ AB. If AB = 20 cm, AD = 13 cm and area of the parallelogram is 100 cm², find AL.