The aspect ratio of the sides of the two squares is 5: 4. If the sides of each square are reduced by two

The aspect ratio of the sides of the two squares is 5: 4. If the sides of each square are reduced by two, then the difference in the areas of the resulting squares will be 28 cm ^ 2. Find the sides of these squares.

Let the side of the first square be X and the side of the second square equal to Y.

Then X / Y = 5/4. (one)

X = 1.25 * Y.

Also, by hypothesis, (X – 2) ^ 2 – (Y – 2) ^ 2 = 28.

Substitute X = 1.25 * Y.

(1.25 * Y – 2) ^ 2 – (Y – 2) ^ 2 = 28.

25 * Y ^ 2/16 – 5 * Y + 4 – Y ^ 2 + 4 * Y – 4 – 28 = 0.

9Y ^ 2/16 – Y – 28 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = (-1) 2 – 4 * 0.5625 * (-28) = 1 + 63 = 64.

X1 = (1 – √64) / 2 * (0.5625) = (1 – 8) / 1.125 = -7 / 1.125 = -56/9. (Doesn’t match because <0).

X2 = (1 + √64) / 2 * (0.5625) = (1 + 8) / 1.125 = 9 / 1.125 = 8 cm.

Y = 1.25 * Y = 10 cm.

Answer: The sides of the squares are 10 cm and 8 cm.