Wednesday, 4 December 2019

Perimeter and Area (Practice Set 44)

Practice Set 44

1)If the length and breadth of a rectangle is doubled, how many times will the perimeter of the new rectangle will that of the original rectangle?
->  Let the length and breadth of the rectangle be x cm and y cm respectively.
∴ perimeter of rectangle = 2X Length + 2X Breadth
                                        = 2 X x + 2 X y
                                        = 2x + 2y
                                        =2 (x+y)

Now if the length and breadth of the new rectangle is doubled then 
length 2x cm and breadth 2y cm
∴ Perimeter of new rectangle = 2X Length + 2X Breadth
                                               = 2 X 2x  +  2 X 2y
                                               = 4x + 4y
                                               = 4(x+y)
here, 4(x+y) is twice 2(x+y)
∴ the perimeter of new rectangle is twice the perimetr of original rectangle.

2) If the side of a square is tripled. how many times its perimeter will be that of the original square.
-> Let the side of a square be x cm
∴ the perimeter of a square = 4 X side
                                            =  4 X x
                                            =  4x cm
Now, If the side of a square is tripled, =3x
then, the perimeter of new square = 4 X side
                                                      = 4 X 3x
                                                      = 12x cm
12x cm is three times 4x cm
∴ the perimeter of a new square is three times the perimeter of the original rectangle.

3) The figure of a playground is given.
 The length of the sides are given.
Find the perimeter of the playground.  

-> AP = AB + BP  (∵ CD = BP)
           = AB + CD
           = 10 + 5
     AP = 15 m
     EF = 15 m

PE = PD + DE  (∵ BC = PD)
      = BC + DE
      = 15 + 15
  PE  = 30 m
  AF = 30 m
∴ the perimeter of the playground
= AP + PE + EF + AF
= 15 + 30 + 15 + 30
= 90 m

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