In the figure,

DE||BC
if

DE=4 cm,BC=8 cm
and area (ΔADE)=25cm2, then the area of

ΔABC
is ____ cm

2

.

Question

In the figure,

DE||BC
   if

DE=4 cm,BC=8 cm
   and area (ΔADE)=25cm2, then the area of

ΔABC
   is ____ cm

2

.

Accepted Answer

In the figure

DE‖BC
  if

DE=4 cm,BC=8 cm
   and area (ΔADE)=25cm2, then the area of

ΔABC
   is 100 cm

2

. In the given figure DE||BC, DE=4 cm, BC=8cm and area of (ΔADE)=25cm2We know,The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.In the triangles

Δ
  ABC

andΔ
  ADE, the sides DE and BC are parallel and AB is transversal, corresponding angles are equal. So,

∠
  B

=∠
  D As the sides DE and BC are parallel and AC is transversal, corresponding angles are equal. So,

∠
  C

=∠
  E As the angles,

∠
  BAC

and∠
  DAE are the common angles of both triangles. So, the triangles

Δ
  ABC

andΔ
  ADE are similar by the AAA criterion.Now,If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.Therefore,

ar
        
         ΔADE

ar
        
         ΔABC

=

DE
        2

BC
        2

⇒
      
       25
      
       ar
        
         ΔABC

=

4
         
        2

8
         
        2

⇒
      
       25
      
       ar
        
         ΔABC

=
      
       16
      
       64

⇒ar
      
       ΔABC
     =100 
      cm
      2

The area of

Δ
  ABC is 100 cm .

In the figure, $DE||BC$ if $DE = 4 cm, BC = 8 cm$ and area (ΔADE)=25 $c m^{2}$ , then the area of $Δ ABC$ is ____ cm $2$ .

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In the figure, DE||BC if DE=4 cm,BC=8 cm and area (ΔADE)=25cm2, then the area of ΔABC is ____ cm 2 .