Proportional Reasoning 1 Class 8 Long Question Answer

Proportional Reasoning 1 Class 8 Long Question Answer

Proportional Reasoning 1 Class 8 Long Question Answer

Question 1.

In Fig. (i) and Fig. (ii), find the ratio of the area of the shaded portion to that of the whole figure :

Solution:

(i) For Fig. (i),

Area of the whole region

= 4 × 4 = 16 sq. units

and area of the shaded region

= 8 sq. units So, required ratio

= 8 : 16 = 1: 2.

For Fig. (ii),

Area of the whole region

= 16 sq. units (By counting the squares)

and area of the shaded region = 8 sq. units (By counting the squares) (As 2∆ = 1 square)

So, required ratio

= 8 : 16 = 1 : 2.

Question 2.

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

Solution:

(a) Perimeter of shaded portion

= 2(120 + 120) cm

= 480 cm [2 × 60 = 120 and 3 × 40 = 120]

Perimeter of whole region

= 2(240 + 200) cm

= 880 cm [4 × 60 = 240 and 5 × 40 = 200]

So, required ratio

= 480 : 880 = 48 : 88 = 6 : 11.

(b) Area of the shaded portion

= 120 × 120 = 14400 sq. cm.

Area of the whole portion ,

= 240 × 200 = 48000 sq. cm.

So, area of the unshaded portion

= 48000 - 14400

= 33600 sq. cm.

Thus, required ratio

= 14400 : 33600

= 144 : 336 = 12 : 28

= 3 : 7.