Question

find the area of square the length of whose diagonal is 9.6 metre​

Answer 1

$\bf{\underline{Answer :- }}$

Area of the square is 46.08 m²

$\bf{\underline{Explanation :- }}$

Length of the diagonal of the square ( d ) = 9.6 m

Let the length of the side of the square be 's' m

Now, let us draw a square with diagonal ( Refer the attachment )

Consider the Δ ABD

We know that all angles in square measures 90°. So, ∠BAD = 90°

Therefore Δ ABD is a right troangle

$\tt By \ pythagoras \ theorem \\ \\ \sf \implies AB^2 + AD^2 = BD^2 \\ \\ \sf \implies s^2 + s^2 = 9.6^2 \\ \\ \sf \implies 2s^2 = 9.6^2 \\ \\ \tt Taking \ square \ root \ on \ both \ sides \\ \\ \sf \implies \sqrt{2s^2 } = \sqrt{9.6^2 } \\ \\ \sf \implies \sqrt{2}s = 9.6 \\ \\ \sf \implies s = \dfrac{9.6}{ \sqrt{2} }$

$\sf Area \ of \ the \ square = s^2 \\ \\ \sf = \bigg( \dfrac{9.6}{ \sqrt{2} } \bigg)^2 \\ \\ \sf = \dfrac{9.6^2 }{( \sqrt{2})^2} \\ \\ \sf = \dfrac{92.16}{2} \\ \\ \sf = 46.08 \ m^2$