The width of the rectangle is 6 cm less than the length and its density is 40 cm ^ 2. find the sides of the rectangle.

Let the length of the rectangle be (x) cm, then the width is (x – 6) cm.The area of the rectangle is (x (x – 6)) cm ^ 2 or 40 cm ^ 2. Let’s make an equation and solve it.

x (x – 6) = 40;

x ^ 2 – 6x = 40;

x ^ 2 – 6x – 40 = 0;

D = b ^ 2 – 4ac;

D = (-6) ^ 2 – 4 * 1 * (-40) = 36 + 160 = 196, √D = √196 = 14;

x = (-b ± √D) / (2a);

x1 = (6 + 14) / (2 * 1) = 20/2 = 10 (cm) – length;

x2 = (6 – 14) / (2 * 1) = -8/2 = -4 (cm) – length cannot be expressed as a negative number.

x – 6 = 10 – 6 = 4 (cm) – width.

Answer. 4 cm, 10 cm.