In a floral design made from tiles each of dimensions 40cm by 60cm (See Fig. 8.7), 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.

Length of the tiles is 40 cm.

∴ One part of length =

Width of the tiles = 60 cm

One part of width =

There are two part of length and three parts of width.

Length of shaded portion = 2× 10 = 20 cm

Width of shaded portion = 3× 12 = 36 cm

a) Perimeter of shaded portion = 2(20+36) = 2× 56 = 112 cm

Perimeter of whole design = 2(40+60) = 2× 100 = 200 cm

Ratio of the perimeter of shaded portion to the perimeter of the whole design =

Ratio = 14:25

b) Area of shaded portion = 20× 36 = 720 sq. cm

Area of unshaded portion = area of whole figure – area of shaded portion

= 40× 60 – 720

= 2400 – 720 = 1680 sq. cm

Ratio of the area of the shaded portion to the area of the unshaded portion =

Ratio = 3:7