(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