If $△ A B C \sim △ D E F$ and $A B : D E = 3 : 4$ , then the ratio of area of triangles taken in order is

\frac{9}{16}

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\frac{16}{9}

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\frac{15}{9}

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\frac{9}{15}

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Solution

The correct option is A $\frac{9}{16}$
In similar triangles,
Ratio of areas of triangle = Square of ratio of corresponding sides
Ratio of areas of triangle= $\frac{3^{2}}{4^{2}}$

= $\frac{9}{16}$

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Similar questions

Q. In a triangle ABC, a:b:c=4:5:6, then the ratio of circumradius to inradius will be .

The sides of $Δ ABC$ are 9 cm, 15 cm and 18 cm. Find the perimeter of the smaller triangle which is similar to $Δ ABC$ if the ratio of corresponding sides is 3.

△ A B C \sim D E F

. If area of

△ A B C = 9 s q . c m

., area of

△ D E F = 16 s q . c m

and

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, find the length of

E F

Q. Question 9
Tick the correct answer and justify:
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio

(A) 2 : 3
(B) 4 : 9
(C) 81 : 16
(D) 16 : 81

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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If △ABC∼△DEF and AB:DE=3:4, then the ratio of area of triangles taken in order is

The correct option is A 916 In similar triangles,Ratio of areas of triangle = Square of ratio of corresponding sidesRatio of areas of triangle=3242 =916

If $△ A B C \sim △ D E F$ and $A B : D E = 3 : 4$ , then the ratio of area of triangles taken in order is

The correct option is A $\frac{9}{16}$
In similar triangles,
Ratio of areas of triangle = Square of ratio of corresponding sides
Ratio of areas of triangle= $\frac{3^{2}}{4^{2}}$

= $\frac{9}{16}$