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