Q. 18 A4.5( 4 Votes )

# Area of field in the shape of parallelogram ABCD is 96 sq. cm., length of diagonal BD is 12 cm. What is the perpendicular length drawn on diagonal BD from the point A?

Answer :

Let us consider a parallelogram ABCD such that

Area(ABCD) = 96 cm^{2} and BD = 12 cm

To find: length of perpendicular length drawn on diagonal BD from the point A i.e. AE.

Now, In ΔABD and ΔBCD,

AB = CD [Opposite sides of parallelogram are equal]

AD = BC [Opposite sides of parallelogram are equal]

BD = BD [Common]

ΔABD ≅ ΔBCD [By SSS congruency criterion]

[Congruent triangles have equal areas]

⇒

Now, we know

Area of a triangle

⇒ 6AE = 48

∴ AE = 8 cm

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