Question

The area of a square field is 0.5 hectare. The length of its diagonal is

(a) 100 m
(b) 50 m
(c) 250 m
(d) $50\sqrt{2}$ cm

Answer 1

(a) 100 m

Area of the square = $\left\{\frac{1}{2}\times {\left(D\mathrm{iagonal}\right)}^2\right\}$sq. units.
Given:
Area of square field = 0.5 hectare
= $\left(0.5\times 10000\right)$m² [since 1 hectare = 10000 m²]
= 5000 m²

Diagonal of a square = $\sqrt{2\times \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{square}}$
= $\left(\sqrt{2\times 5000}\right)$m = 100 m
Hence, the length of the diagonal of a square field is 100 m.