In the given figure, $△ A B C$ and $△ D E F$ are similar. BC = 3 cm, EF = 2 cm, and area of $△ A B C = 54 c m^{2}$ , then the area of $△ D E F$ is __ $c m^{2} .$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 24
We know that the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

$△ A B C$ $\sim$ $△ D E F$ (given)

$\Rightarrow \frac{A r e a o f △ A B C}{A r e a o f △ D E F} = \frac{B C^{2}}{E F^{2}}$

$\frac{54}{A r e a o f △ D E F} = \frac{3^{2}}{2^{2}}$

$\frac{54}{A r e a o f △ D E F} = \frac{9}{4}$

$A r e a o f △ D E F = \frac{4 \times 54}{9} = 4 \times 6 = 24 c m^{2}$

Suggest Corrections

Similar questions

In given figure $△ A B C$ and $△ D E F$ are similar, $B C = 3 c m$ , $E F = 4 c m$ , and area of triangle $A B C = 54 c m^{2}$ find the area of $△ D E F$ in __ $c m^{2}$

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.

Join BYJU'S Learning Program

In the given figure, △ABC and △DEF are similar. BC = 3 cm, EF = 2 cm, and area of △ABC=54 cm2, then the area of △DEF is __ cm2.

The correct option is C 24We know that the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides. △ABC ∼ △DEF (given) ⇒Area of △ABCArea of △DEF=BC2EF2 54Area of △DEF=3222 54Area of △DEF=94 Area of △DEF=4×549=4×6=24 cm2

In the given figure, $△ A B C$ and $△ D E F$ are similar. BC = 3 cm, EF = 2 cm, and area of $△ A B C = 54 c m^{2}$ , then the area of $△ D E F$ is __ $c m^{2} .$