In given figure $△$ ABC and $△$ DEF are similar, EF=3cm, BC=4cm, and area of triangle DEF=54 $c m^{2}$ . Find the area of $△$ ABC.

___ $c m^{2}$ .

98 $c m^{2}$

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30.3 $c m^{2}$

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82 $c m^{2}$

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96 $c m^{2}$

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Solution

The correct option is D
96 $c m^{2}$

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

So $\frac{9}{16}$ = $\frac{54}{a r e a o f △ A B C}$

Area of $△$ ABC = 96 $c m^{2}$

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Similar questions

In the given figure $△$ ABC and $△$ DEF are similar, EF=3cm, BC=4cm, and area of triangle DEF=54 $c m^{2}$ find the area of $△$ ABC

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In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ . Find the area of $△$ DEF. (Note: The given figures are not to scale.)

c m^{2}

If $△$ ABC is similar to $△$ DEF such that BC = 3 cm, EF = 4 cm and area of $△$ ABC = 54 ${c m}^{2}$ . Determine the area of $△$ DEF.

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In given figure △ ABC and △ DEF are similar, EF=3cm, BC=4cm, and area of triangle DEF=54cm2 . Find the area of △ ABC. ___ cm2.

The correct option is D 96 cm2 We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. So 916 =54area of △ABC Area of △ ABC = 96 cm2

In given figure $△$ ABC and $△$ DEF are similar, EF=3cm, BC=4cm, and area of triangle DEF=54 $c m^{2}$ . Find the area of $△$ ABC.

___ $c m^{2}$ .

The correct option is D
96 $c m^{2}$

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

So $\frac{9}{16}$ = $\frac{54}{a r e a o f △ A B C}$

Area of $△$ ABC = 96 $c m^{2}$