3 x 14 = 42 (Twice of AB)
42 divided by 2 = 21
21 x 3 = 63
Pie x 14 = circumference = 44
44 divided by 2 = 22 (circumference of semicircle)
(22 + 22 + 22) x 2 = 132
132 + 21 + 21 + 63 = 237
Ans: 237cm

Not correct. AB isn't ⅓ of the length. You'll end up with the length and breadth being the same but question mentioned the ratio is 3 : 2.

And the question asked to find the perimeter of the paper in figure 1 but you were calculating the perimeter of figure 2 (which you left out 1 breadth in your calculation also)


Ratio of length to breadth = 3 : 2

Ratio of AB to breadth = 1 : 3

Since the breadth did not change/wasn't altered, the number of units should be the same for both ratios.

We make them the same.

Multiply by 3,
Ratio of length to breadth = 9 : 6

Multiply by 2,
Ratio of AB to breadth = 2 : 6


So breadth is actually 6 units. AB is actually 2 units and length is 9 units.

Difference between length and AB
= 9 units - 2 units = 7 units


Now notice that 7 units is the same as 3 diameters of a semicircle.

7 units = 3 x 14cm = 42cm

1 unit = 42cm ÷ 7 = 6cm

Perimeter of rectangle in figure 1
= 2 lengths + 2 breadths
= 2 x 9 units + 2 x 6 units
= 18 units + 12 units
= 30 units

= 6cm x 30 = 180cm

Another way to find AB :

14cm x 3 = 42cm

Length = AB + 42cm (as deduced from diagram)

Breadth = 3 x AB (given)


Since ratio of length to breadth = 3 : 2,

2 x length = 3 x breadth
(both sides are now 6 units)

2 x (AB + 42cm) = 3 x 3 x AB

2 x AB + 84cm = 9 x AB

Since 9 - 2 = 7,
This tells us that 7 x AB = 84cm

AB = 84cm ÷ 7 = 12cm




Length = 12cm + 42cm = 54cm
Breadth = 12cm x 3 = 36cm

Perimeter = 36cm + 54cm + 54cm + 54cm
= 180cm