Question

In triangle ABC „DE parallel to AB,
AD=3DC, ACABED) = 90 cm²
Find A Ctriangle ABC).​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The area of triangle ABC is 96 cm².

In Triangle ∆ABC, DE || AB , AD = 3DC , Area of (ABED) = 90 cm².

We have to find the Area of triangle, ∆ABC.

Construct :

• Draw a triangle ABC where AB is its base (not mandatory but to solve easily we do it).
• Now make DE parallel to AB.
• It has given that AD = 3DC , from Thales’ theorem, BE = 3EC.
• ∴ AD/AC = BE/BC = 1/(1 + 3) = 1/4

Concept :

• Basic proportionality theorem : The line drawn parallel to one side of a triangle and cutting the other two sides divides two sides in equal proportions.
• Area of triangle for two similar triangle : If we draw a line parallel to one side of triangle cutting other two sides, we get two similar triangle and ratio of area of these triangle is square of ratio of their corresponding sides.

from above concept,

∆CDE and ∆CAB are similar.

∴ Ar(∆CDE)/Ar(ABC) = (AD/AC)²

∵ AD/AC = 1/4 and Ar(∆ABC) = Ar(∆CDE) + Ar(ADEB)

but Ar(ADEB) = 90 cm²

Let Ar(∆CDE) = x

⇒x/(x + 90) = (1/4)² = 1/16

⇒16x = x + 90

⇒15x = 90

⇒x = 6

now, the area of triangle ∆ABC = x + 90 = 96 cm²

Therefore the area of triangle is 96 cm².