The diagonal of a square measures $6\sqrt{2}$cm. The measure of the diagonal of a square whose area is twice that of the first square is:
Answer & explanation
Correct answer: option 1
We know that,
Diagonal of square = \(\sqrt {2}\) × Side of square
We have,
The diagonal of the square = 6\(\sqrt {2}\) cm
So, \(\sqrt {2}\) × Side of square = 6\(\sqrt {2}\)
Side of square = 6 cm
Area of first square = 6 × 6 = 36 cm2
Area of second square = 2 × 36 = 72 cm2
The side of the second square = \(\sqrt {72}\) = 6\(\sqrt {2}\)
The diagonal of second square = \(\sqrt {2 × area of square }\) = \(\sqrt {2 × 72 }\) = \(\sqrt {144}\) = 12