The area of a square is 144 sqcm. Find the length of the diagonal.
The correct answer is B. 12√2 cm
The area of a square is given by the formula `Area = side^2`, where `side` is the length of a side of the square. In this case, the area of the square is given as 144 sqcm, so we can write the equation:
`side^2 = 144`
Solving for `side`, we get:
`side = sqrt(144) = 12`
So, the length of a side of the square is 12 cm.
The diagonal of a square divides it into two 45-45-90 right triangles. In such a triangle, the length of the hypotenuse (the diagonal of the square) is `sqrt(2)` times the length of a leg (a side of the square). Therefore, the length of the diagonal of the square is:
`diagonal = side √2 =12 x √2= 12√2
So, the length of the diagonal of the square is 12√2 cm,.
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