Question

ABCD is a parallelogram in which de is perpendicular to ab . If ab is equal to 8cm and ad is equal to 5cm , the area of the parallelogram is 24cm square , find AE

Answer 1

If ab is equal to 8cm and ad is equal to 5cm, the area of the parallelogram is 24cm square, then the length of AE is 4 cm.

Step-by-step explanation:

It is given that,

ABCD is a parallelogram

Side AB = 8 cm

Side AD = 5 cm

Area of the parallelogram = 24 m²

DE ⊥ AB

We know that the formula of the area of a parallelogram is given by,

Area = Base × Perpendicular Height  

From the figure attached below, we have

Side AB = 8 cm and the perpendicular height corresponding to this side is DE.

So, substituting the values in the formula, we get

Area = AB × DE  

⇒ 24 = 8 × DE

⇒ DE = $\frac{24}{8}$

⇒ DE = 3 cm

Now, considering the right-angled triangle DEA, and applying the Pythagoras theorem, we get

AD² = DE² + AE²

⇒ AE = $\sqrt{AD^2 - DE^2}$

⇒ AE = $\sqrt{5^2 - 3^2}$

⇒ AE = $\sqrt{25 - 9}$

⇒ AE = $\sqrt{16}$

⇒ AE = 4 cm

Thus, the length of AE is 4 cm.

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