The side of one square is 2 cm longer than the side of a second square. If the combined area of the squares is 100 square cm, find the dimensions of each square. : The area of the two squares x^2 + (x+2)^2 = 100 x^2 + x^2 + 4x + 4 = 100 2x^2 + 4x + 4 - 100 = 0 2x^2 + 4x - 96 = 0 Simplify, divide by 2
x^2 + 2x - 48 = 0 Factors to (x+8)(x-6) = 0 the positive solution x = 6 : 6 by 6 the small square 8 by 8 the large square ; : Check: 36 + 64 = 100 Does this make sense to you?
