The length of a rectangular garden is 20 m and its breadth is 8 m. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden.

Given:

Length of rectangular garden (l) = 20 m

Breadth of rectangular garden (b) = 8 m

Formula Used:

Area of a rectangle = length × breadth

Area of a square = side × side = s²

Diagonal of a square = s\(\sqrt{2}\)

Calculation:

Area_rectangle = l × b = 20 m × 8 m = 160 m²

Area_square = 160 m²

Side (s) of the square garden:

s² = 160

s = \(\sqrt{160}\)

s = \(\sqrt{16 \times 10}\)

s = 4\(\sqrt{10}\) m

Length of the diagonal of the square garden:

Diagonal = s\(\sqrt{2}\)

Diagonal = (4\(\sqrt{10}\)) × \(\sqrt{2}\)

Diagonal = 4\(\sqrt{10 \times 2}\)

Diagonal = 4\(\sqrt{20}\)

Diagonal = 4\(\sqrt{4 \times 5}\)

Diagonal = 4 × 2\(\sqrt{5}\)

Diagonal = 8\(\sqrt{5}\) m

∴ The length of the diagonal of the square garden is 8\(\sqrt{5}\) m.