Read the following situation and answer the questions that follow.
A rectangular garden has numerical length ℓ metres and breadth b metres. The perimeter of the garden is 26 metres and its area is 40 square metres.
(i) Express ℓ and b in terms of their sum and product, and write down these two numerical values.
(ii) Taking ℓ and b as the zeros, construct the monic quadratic polynomial whose zeros represent the two dimensions of the garden.
(iii) Factorise the polynomial of part (ii) to determine the exact numerical values of ℓ and b.
(iv) Show that the dimensions you have obtained satisfy both the given perimeter and area conditions.