The length of the rectangle is 13 cm longer than its width. The width of the rectangle is 140 cm2. Find the perimeter of the rectangle.

Let’s denote the width of the rectangle as x, then the length of the rectangle will be equal to x + 13. We know the area of ​​the rectangle, so we can find the sides. To do this, substitute the known values ​​into the formula for finding the area of ​​a rectangle:

S = a * b, where S is the area, a and b are the sides of the rectangle.

140 = x * (x + 13);

we solve this equation:

140 = x ^ 2 + 13x;

x ^ 2 + 13x – 140 = 0.

Next, we solve the quadratic equation:

D = b ^ 2 – 4ac = 13 ^ 2 – 4 * 1 * (-140) = 169 + 560 = 729 = 27 ^ 2.

x1 = (-13 + 27): 2 = 14: 2 = 7;

x2 = (-13 – 27): 2 = -40: 2 = -20.

since the width cannot be a negative number, then only the first root is suitable for us. Knowing the width, we can find out the length:

7 + 13 = 20 (cm).

We can now find the perimeter:

P = (a + b) * 2 = (7 + 20) * 2 = 27 * 2 = 54 (cm).

Answer: The perimeter of the rectangle is 54 cm.