How many times will the area of a square increase if its diagonal is increased 1.5 times?

To find out the change (increase) in the area of the square under consideration, consider the ratio: ΔS = Sk / Sn = 0.5dk ^ 2 / 0.5dn ^ 2 = dk ^ 2 / dn ^ 2 = (dk / dn) ^ 2 = k ^ 2 …

Data: k is the ratio of the lengths of the diagonals (k = 1.5 p.).

Let’s perform the calculation: ΔS = k ^ 2 = 1.5 ^ 2 = 2.25 p.

Answer: The area of the square in question should have increased by 2.25 times.