# The perimeter of the rectangle is 240 cm. If the length of the rectangle is reduced by 14 cm and the width is increased by 10 cm

The perimeter of the rectangle is 240 cm. If the length of the rectangle is reduced by 14 cm and the width is increased by 10 cm, then its area will increase by 4 cm2. Find the sides of the rectangle.

Find the sum of the length and width of the starting rectangle.
We divide the perimeter into 2 parts.
240/2 = 120 cm.
We write the length as the unknown value of x, and the width as y.
The sum of the lengths of the sides will be:
x + y = 120.
The starting area will be:
x * y.
If you reduce the length by 14 cm, it will be:
x – 14 cm.
With an increase in width by 10 cm, it will be equal to:
y + 10.
The area will be:
(x – 14) * (y + 10) = x * y + 10 * x – 14 * y – 140.
The area difference will be:
x * y + 10 * x – 14 * y – 140 – x * y = 4.
10 * x – 14 * y – 140 = 4.
Express x from the perimeter.
x = 120 – y.
Substitute the area difference into the equation.
10 * (120 – y) – 14 * y – 140 = 4.
1200 – 10 * y – 14 * y – 140 = 4.
-24 * y = -1056.
y = 1056/24 = 44 cm (width).
x = 120 – 44 = 76 cm (length).

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