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$Δ D E F ~ Δ A B C$ , if $D E : A B = 2 : 3$

and $ar (Δ D E F)$ is equal to 44 square units. Find the ar $(Δ ABC)$ .

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121

answer is B.

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Detailed Solution

Given that

ar (Δ D E F)

= 44 square units
And

Δ D E F ~ Δ A B C

D E : A B = 2 : 3

Find the ar

(Δ A B C)

Use the theorem of areas of triangle: Ratio of area of similar triangles is equal to the ratio of the square of its corresponding sides.
Now,

ar (Δ D E F) ar (Δ A B C) = (D E) 2 (A B) 2

⇒ 44 ar (Δ A B C) = (2) 2 (3) 2 ⇒ 44 ar (Δ A B C) = 49 ⇒ ar (Δ A B C) = 44 × 9 4 ⇒ ar (Δ A B C) = 99 square units

Δ D E F ~ Δ A B C,

if D

E : A B = 2 : 3

and

ar (Δ D E F)

is equal to 44 square units, then the ar

(Δ ABC)

is 99 square units.
Therefore, option 2 is correct.

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