Question

Find the length of diagonal of a square with side 8 cm.

Answer 1

Suppose ABCD is a square of side 8 cm.

Here, segment AC is a diagonal of square ABCD.

In ∆ABC,

l(AC)² = l(AB)² + l(BC)²              ...(Pythagoras theorem)

⇒ l(AC)² = (8)² + (8)² 

⇒ l(AC)² = 64 + 64 = 128

⇒ l(AC) = \[\sqrt{128}\] cm        …[Taking square root of both sides]

⇒ l(AC) = \[\sqrt{64 × 2}\] cm

⇒ l(AC) = 8\[\sqrt{2}\] cm

Thus, the length of diagonal of square is 8\[\sqrt{2}\] cm.