<span>The line of symmetry of the triangle bisects the right angle and the diagonal of the square. The line is 1/2 the length of the square's diagonal :
(1/2)(10√2) = 5√2.
</span>Let CG be a distance x from the vertex of the right angle in the triangle. Remaining distance = 5√2 - x. <span> (1)(x) = (2)(5√2 - x)</span> x = 10√2 - 2x <span>3x = 10√2 </span> <span>x = (10/3)√2. </span> Using Pythagorean theorem, x^2 + y^2 = c^2
<span>c = (10/3)√2, and x = y, so 2x^2 = 200/9 x = √(100/9) = 10/3 = y. </span> <span>x = y = 3.333</span>
Let the number of cards in each group be 2x and 3x. So, 2x + 3x = 120 5x = 120 x = 120 / 5 x = 24 Number of cards in each group is 2x = 2 × 24 = 48 3x = 3 × 24 = 72
