Question

In triangle ABC and triangle DEF are similar where bc=3cm and ef=4cm and the area of the triangle ABC is 54cm square then find the area of the triangle DEF

Answer 1

Answer:

I don't know the a answer

Answer 2

Step-by-step explanation:

GIVEN:-

• $BC=3cm$
• $EF=4cm$
• $Area(ΔABC)=54{cm}^{2}$

NEED TO FIND:-

• $Area(ΔDEF)=?$

SOLUTION:-

We know that,

Ratio of the area of two triangles is equal to the ratio of sqaure of their corresponding sides.

$\color{blue}{\frac{ Ar.(ΔABC) }{Ar.(DEF)} = ({ \frac{AB}{DE} })^{2} = ({ \frac{EF}{BC} })^{2} = ({ \frac{AC}{DF} })^{2}}$

$\frac{Ar.(ΔABC)}{Ar.(ΔDEF) } = ({ \frac{BC}{EF} })^{2}$

$\frac{54}{Ar.(ΔDEF) } = ( { \frac{3}{4} })^{2}$

$\frac{54}{Ar.(ΔDEF) } = \frac{9}{16}$

$Ar.( ΔDEF ) = 54 \times \frac{16}{9}$

$Ar.( ΔDEF ) = 6 \times 16$

$Ar.( ΔDEF ) = 96 {cm}^{2}$

HOPE THAT HELPS!!