Triangle XYZsim triangle DEF the correspondence XYZ leftrightarrow EFD- If XY-EF -2-3 and the area triangle XYZ is 18- then the area of triangle DEF is -1840-53648

Question

Toppr Admin · Accepted Answer

-x21D2-area-xA0-of-xA0-x25B3-XYZarea-xA0-of-xA0-x25B3-DFF-XY2EF2-x21D2-xA0-18-x25B3-DEF-49area-xA0-x25B3-DEF-9-xD7-92-40-5

$△ X Y Z \sim △ D E F$ for the correspondence XYZ $\leftrightarrow$ EFD, If $X Y : E F = 2 : 3$ and the area $△ X Y Z$ is $18$ , then the area of $△ D E F$ is ............
$18$
$40.5$
$36$
$48$

$\Rightarrow \frac{a r e a o f △ X Y Z}{a r e a o f △ D F F} = \frac{X Y^{2}}{E F^{2}}$
$\Rightarrow \frac{18}{△ D E F} = \frac{4}{9}$
$a r e a (△ D E F) = \frac{9 \times 9}{2} = 40.5$

△XYZ∼△DEF for the correspondence XYZ ↔ EFD, If XY:EF=2:3 and the area △XYZ is 18, then the area of △DEF is ............1840.53648

⇒area of △XYZarea of △DFF=XY2EF2⇒ 18△DEF=49area (△DEF)=9×92=40.5

$△ X Y Z \sim △ D E F$ for the correspondence XYZ $\leftrightarrow$ EFD, If $X Y : E F = 2 : 3$ and the area $△ X Y Z$ is $18$ , then the area of $△ D E F$ is ............
$18$
$40.5$
$36$
$48$

$\Rightarrow \frac{a r e a o f △ X Y Z}{a r e a o f △ D F F} = \frac{X Y^{2}}{E F^{2}}$
$\Rightarrow \frac{18}{△ D E F} = \frac{4}{9}$
$a r e a (△ D E F) = \frac{9 \times 9}{2} = 40.5$