Question

In a design made from tiles each of dimensions 40cm by 60cm,find the ratios of:
a)the perimeter of shaded portion to the perimeter of the whole design.
b)the area of the shaded portion to the area of the unshaded portion​

Answer 1

★Given :

• Length of tile = 60cm
• Breadth of tile = 40cm

★To find :

• The perimeter of shaded portion to the perimeter of the whole design.
• The area of the shaded portion to the area of the unshaded portion

★Solution :

Let us take 1 tile as 1 unit.

Now,

For the shaded portion :

• Length = 3units
• Breadth = 2units

Perimeter = 2(l+b)

                =2(3+2)

               = 10 units

Therefore,

• Perimeter of shaded portion = 10units

Area = l×b

       = 3(2)

        = 6sq units

Therefore,

• Area of shaded portion = 6 sq. units

For the whole design :

• Length = 5units
• Breadth = 4units

Perimeter = 2(l+b)

                =2(5+4)

               = 18units

Therefore,

• Perimeter of whole design = 18units

Area = l×b

       = 5(4)

        = 20sq units

Therefore,

• Area of whole design = 20 sq. units

And,

Area of unshaded portion = Total area - Area of the shaded portion

→20 - 6

→ 14 sq. units

~To find Ratio of perimeter of the shaded portion to the perimeter of the whole design :

→Perimeter of shaded portion/Perimeter of whole design

→10/18

→5/9

→5 : 9  

~To find Ratio of area shaded portion to the area of unshaded portion :

→Area of shaded portion/Area of unshaded portion

→ 6/14

→ 3/7

→ 3 : 7

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