## 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.

-> 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

Hi

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