The diagonal of the square is $8\sqrt{2}$ cm. Find the diagonal of another square whose area is triple that of the first square.
Answer & explanation
Correct answer: option 4
We know that,
Area of a square = (Side)2
Diagonal of a square is = Side\(\sqrt {2}\)
The diagonal of the first square is = 8\(\sqrt {2}\)
As given in the question, diagonal = 8\(\sqrt {2}\)= side\(\sqrt {2}\)
= The side of the first square = 8 cm
= The area of the first square = (8)2 = 64 cm2
The Area of the Second square is double the first one
= Area of the second one = 64×3
= Side of the 2nd square = \(\sqrt {64 × 3}\) = 8×\(\sqrt {3}\)
The diagonal 2nd square = \(\sqrt {2}\)×8×\(\sqrt {3}\) = $8\sqrt{6}$ cm