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Question
Find the area of a square whose diagonal is `12sqrt(12)"cm"`
Solution
The sides and diagonal of a square form a right triangle as each angle of a square is a right angle.
Diagonal is the side opposite to the right angle, therefore it is the hypotenuse
Here, Diagonal of the square = `12sqrt(2)"cm"`
Let the side of the square = s
∴ `sqrt("s"^2 + "s"^2) = 12sqrt(2)`
⇒ `sqrt(2"s"^2) = 12sqrt(2)`
⇒ `"s"sqrt(2) = 12sqrt(2)`
⇒ s = 12
We know,
The area of a square with side s = s2
∴ s2
= (12)2
= 144cm2.
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