Question

Two rectangles ABCD and DBEF are as shown in the figure. Find the area of
rectangle DBEF .

Answer 1

Answer:

From the figure given, △ADB forms a right angled triangle.

We know that square of hypotenuse of a triangle is equal to sum of squares of adjacent sides.

⇒(BD)

2

=(AB)

2

+(AD)

2

⇒(BD)

2

=(4)

2

+(3)

2

=25

⇒BD=

25

=5

Consider △BCD,

Area of △BCD =

2

1

×BC×CD=

2

1

×BD×CG

⇒BD∗CG=BC∗CD ............(i)

Area of rectangle BDFE=BD×FE=BD×CG=BC×CD (∵FE=CG and eqn (i))

Area of rectangle BDFE=BC×CD=3×4=12

Step-by-step explanation:

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