Saturday 22 June 2013

Numerical Based On Square ( Mathematics )

Q. Find the perimeter of a square with the following area:
  1. 81 m
  2. 36 cm
  3. 49 mm
  4. 16 dm
  5. µm
  6. 9 km
  7. 25 inches
  8. 64 nm
Sol.
1. Area of the Square = 81 m         
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 81 m
               side   =   81 m
                        =  9 m
    ∴   Perimeter of the Square = 4 x ( side ) = 4 x 9 m = 36 m


2. Area of the Square = 36 cm         
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 36 cm
               side   =   36 cm
                        =  cm
    ∴   Perimeter of the Square = 4 x (side) = 4 x 6 cm = 24 cm


3. Area of the Square = 49 mm
        
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 49 mm
               side   =   49 mm
                        =  7 mm
    ∴   Perimeter of the Square = 4 x side = 4 x 7 mm = 28 mm


4. Area of the Square = 16 dm
         
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 16 dm
               side   =  16 dm
                        = 4 dm
    ∴   Perimeter of the Square = 4 x side = 4 x 4 dm = 16 dm


5. Area of the Square = µm
         
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 4 dm
               side   =   4 dm
                        = 2 dm
    ∴   Perimeter of the Square = 4 x side = 4 x 2 dm =8 dm


6. Area of the Square = 9 km
       
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 9 km
               side   =  √ 9 km
                        =  3 km
    ∴   Perimeter of the Square = 4 x side = 4 x 3 km = 12 km


7. Area of the Square = 25 inches
         
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 25 inches
               side   =   25 inches
                        =  5 inches
    ∴   Perimeter of the Square = 4 x side = 4 x 5 inches = 20 inches


8. Area of the Square = 64 nm
         
    Also, Area of the Square = ( side )2
      ∴   ( side ) = 64 nm
               side   =  √ 64 nm
                        =  8 nm
    ∴   Perimeter of the Square = 4 x side = 4 x 8 nm = 32 nm


Q. Find the area of a square with the following perimeter:
  1. 4 m
  2. 8 cm
  3. 12 mm
  4. 16 dm
  5. 36 µm
  6. 40 km
  7. 44 inches
  8. 48 nm
Sol. 
1. Perimeter of the Square = 4 m 
    Also, Perimeter of the Square = 4 x ( side ) 
      ∴  4 x ( side ) = 4 m
                   side  =  ( 4/4 ) m
                            =  1 m
    ∴    Area of the Square = ( side )= ( 1 x 1 ) m = 1 m

2. Perimeter of the Square = 8 cm 
    Also, Perimeter of the Square = 4 x ( side ) 
      ∴  4 x ( side ) = 8 cm
                   side  =  ( 8/4 ) cm
                            =  2 cm
    ∴    Area of the Square = ( side )= ( 2 x 2 ) cm = 4 cm

3. Perimeter of the Square = 12 mm
    Also, Perimeter of the Square = 4 x ( side ) 
      ∴  4 x ( side ) = 12 mm
                   side  =  ( 12/4 ) mm
                            =  3 mm
    ∴    Area of the Square = ( side )= ( 3 x 3 ) mm = 9 mm

4. Perimeter of the Square = 16 dm
    Also, Perimeter of the Square = 4 x ( side ) 
      ∴  4 x ( side ) = 16 dm
                   side  =  ( 16/4 dm
                            =  4 dm
    ∴    Area of the Square = ( side )= ( 4 x 4 ) dm = 16 dm

5. Perimeter of the Square = 36 µm
    Also, Perimeter of the Square = 4 x ( side ) 
      ∴  4 x ( side ) = 36 µm
                   side  =  ( 36/4 ) µm
                            =  9 µm
    ∴    Area of the Square = ( side )= ( 9 x 9 ) µm = 81 µm

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