A square has side 5 cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is _______ cm. A. 18.50 B. 15.10 C. 10.00 D. 8.50

GATE 2019 · General Aptitude · Squares · medium

Answer: Side of the larger square = 10.00 cm

1. Set up the equation: x^2 + 10x + 25 = 4x^2
2. Rearrange into standard quadratic form: 4x^2 - x^2 - 10x - 25 = 0 => 3x^2 - 10x - 25 = 0
3. Solve the quadratic: a=3, b=-10, c=-25 | discriminant = 100 + 300 = 400 | x = (10 +/- 20)/6 | x = 30/6 = 5 (positive root) or x = -10/6 (rejected)
4. Find the larger square's side: Larger side = 5 + 5 = 10 cm