The area of a square is 144 sqcm. Find the length of the diagonal.

Answer Details

To find the length of the diagonal of a square, we need to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In this case, the two legs of the right triangle are the sides of the square, and the hypotenuse is the length of the diagonal. Let's call the length of one side of the square "x". Then, we know that the area of the square is given by: x^2 = 144 sqcm Taking the square root of both sides, we get: x = 12 cm Now, using the Pythagorean theorem, we can find the length of the diagonal: d^2 = x^2 + x^2 = 2x^2 d = sqrt(2x^2) = x * sqrt(2) = 12 * sqrt(2) cm Therefore, the length of the diagonal is 12√2 cm.