Question

The length of a square field is 0.5 hectare. The length of its diagonal is
(a) 150 m
(b) $100\sqrt{2}$
(c) 100 m
(d) $50\sqrt{2}\mathrm{m}$

Answer 1

(c) 100 m

Disclaimer :- The length cannot be in hectare So we used is as area of the square.
Area of the square field $=0.5\times 10000=5000{\mathrm{m}}^2$



The diagonal divides the square into two isosceles right-angled triangles.

Using Pythagoras' theorem, we have:

${\mathrm{Diagonal}}^2=a^2+a^2=2a^2$
Area of a square = $a^2$

∴ Diagonal​$=\sqrt{2\mathrm{area}}=\sqrt{2\times 5000}=\sqrt{10000}=100\mathrm{m}$