Question

In a floral design made from tiles each of dimensions $40cm$ by $60cm$ (See figure), find the ratios of

a) The perimeter of the 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

Length of each tile $=40cm$

and, breadth of each tile $=60cm$

From the above figure, we find that:

The perimeter of shaded portion $=4\times 40+6\times 60=160+360=520cm$

The perimeter of the whole design $=8\times 40+10\times 60=320+600=920cm$

Area of shaded portion $=80\times 180=14400c{m}^2$

Area of whole design $=160\times 240=38400c{m}^2$

Also, area of unshaded portion $=$ Total area $-$ Area of the shaded portion

$=38400-14400=24000c{m}^2$

a) Ratio of perimeter of the shaded portion to the perimeter of the whole design

$=\frac{\text{Perimeter of shaded portion}}{\text{Perimeter of whole design}}$

$=\frac{520}{920}$

$=\frac{52}{92}$

$=13:23$ [on dividing numerator and denominator by $2$]

b) Ratio of area shaded portion to the area of unshaded portion

$=\frac{\text{Area of shaded portion}}{\text{Area of unshaded portion}}$

$=\frac{14400}{24000}$

$=\frac{144}{240}$

$=\frac{12}{20}$

$=3:5$ [on dividing numerator and denominator by $2$]