Question

∆ABC ~ ∆DEF. If AB = 2.4 cm, DE = 1.6 cm, find the ratio of the areas of ∆ABC and ∆DEF. / ∆ABC ~ ∆DEF. जर AB = 2.4 सेमी, DE = 1.6 सेमी, तर ∆ABC आणि ∆DEF च्या क्षेत्रफळांचे गुणोत्तर काढा. * 9 : 4 3 : 5 5 : 4 12 : 8​

Answer 1

Answer:

if both the triangles are similar,

then,

the ratio of area of triangles ABCandDEF=square of ratio of any of the corresponding sides

=(AB/DE)^2

=1.2x1.2/1.4x1.4

= 36/49

Answer 2

Solution :-

given that,

→ ∆ABC ~ ∆DEF .

we know that,

• when two ∆'s are similar, ratio of areas of them is equal to square of their corresponding sides .

so,

→ A(∆ABC) : A(∆DEF) = AB² : DE²

putting given values of AB and DE we get,

→ A(∆ABC) : A(∆DEF) = (2.4)² : (1.6)²

→ A(∆ABC) : A(∆DEF) = 5.76 : 2.56

→ A(∆ABC) : A(∆DEF) = 576 : 256

→ A(∆ABC) : A(∆DEF) = 9 * 64 : 4 * 64

→ A(∆ABC) : A(∆DEF) = 9 : 4 (Ans.)

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