(i)

Perimeter is the total length of an object. Rectangular objects have 2 equal lengths and 2 equal widths

Let l = length and w = width

Perimeter = l+l+w+w = 2l + 2w

497 = 2l + 2w

But length of the farm is 2¹⁄₂ times the width

Convert the mixed fraction 2¹⁄₂ to improper fraction

2¹⁄₂ = (2x2 + 1)/2 = (4+1)/2 = 5/2

But length of the farm is 2¹⁄₂ times the width

l = (5/2) x w

Substite l into the perimeter equation to solve for w

497 = 2(5/2)xw + 2w

497 = 5w + 2w

497 = 7w

Divide both sides by 7

497/7 = 7w/7

71 = w

The width is 71 km

(ii)

From (i)

l = (5/2) x w

w = 71

l = 5/2 x 71

l = 177.5

The width is 177.5 km

ALTERNATIVELY

497 = 2l + 2w

w = 71

497 = 2l + 2 x 71

497 = 2l + 142

497 - 142 = 2l

355 = 2l

Divide both sides by 2

355/2 = 2l/2

177.5 = l

Length = 177.5 km

(i)

Find the missing dimensions.

a + 3 = 5

a = 5 - 3 = 2

b + 5 = 8

b = 8 - 5 = 3

Add all the sides:

Perimeter = 8 m + 5 m + b + a + 5 m + 3 m

But a = 2 and b = 3

So, Perimeter = 8 m + 5 m + 3 m + 2 m + 5 m + 3 m = 26 m

(ii)

Divide the rooms into two parts and calculate the area of each part.

Area of a rectangle = Length x Breadth

Method I

Part A

Area of A = 5m x 3 m = 15 m²

Part B

Area of B = 5m x 3 m = 15 m²

Total area = Area of A + Area of B

Total area = 15 m² + 15 m² = 30 m²

Method II

Part A

Area of A = 3 m x 2 m = 6 m²

Part B

Area of B = 8 m x 3 m = 24 m²

Total area = Area of A + Area of B

Total area = 6 m² + 24 m² = 30 m²

(iii)

Cost of carpeting the floor = Total area x Cost per square metre

Cost of carpeting the floor = 30 x GH₵ 20.00 = GH₵ 600.00