Question

find the length of the diagonal of a square of side 8cm​

Answer 1

Let XYWZ be the square of side 8cm. seg XW is a diagonal. In ∆ XYW, m∠XYW = 90° … [Angle of a square] ∴ [l(XW)]2 = [l(XY)]2 + [l(YW)]2 …[Pythagoras theorem] = (8)2 + (8)2 = 64 + 64 ∴ [l(XW)]2 = 128 ∴ l(XW) = √128 …[Taking square root of both sides] = √64 × 2 = 8 √2 cm ∴ The length of the diagonal of the square is 8 √2 cm.

Answer 2

Answer:

The length diagonal of diagonal can be found by Pythagoras Theorem as follows :

Let the side be S, then, $Diagonal^2=S^2+S^2$

$\sf Diagonal^2= 8^2+8^2= 2 \times 8^2= 2 \times 64 \\\\\sf Diagonal=\sqrt{2 \times 64} \\\\\sf 8 \sqrt{2} cm$

The length of diagonal is $8 \sqrt{2} cm$