4. A room 6 m long, 4 m wide is surrounded by a verandah. Find the
width of the verandah, if it occupies
24 square metre.
5. A garden 18 m long and 15 m wide is
surrounded by a path 3 m wide. Find the
area of the path
The diagram shows a field with
measurements in metres. Find the area
of the field.
18​

Width of verandah = 1 m

Area of path = 234m²

Explanation:

Dimension of room :

6m by 4m

(6m * 4m) = 24m²

(6 + 2x)(4 + 2x) - 24 = 24

24 + 12x + 8x + 4x² - 24 = 24

4x² + 20x = 24

4x² + 20x - 24 = 0

x² + 5x - 6 = 0

x² + 6x - x - 6 = 0

x(x + 6) -1(x + 6) = 0

(x + 6) = 0 or (x - 1) = 0

x = - 6 or x = 1

x can't be negative, hence x = 1

B.)

Dimension of garden :

18 m by 15 m

Area of garden = 18 m * 15 m = 270 m²

Width of path which surrounds garden = 3m

Hence, dimension of path :

Area of garden and path

(18 +3 + 3)m by (15+3 + 3)m

24m by 21m

Area of path and garden = area of rectangle

Area of rectangle = Length * width

Area of rectangle = 24m * 21m

Aewa of path and garden = 504m²

.

Area of path :

Area of path and garden - Area of garden

504m² - 270m²

= 234m²