One side of the rectangle is 2 m shorter than the doubled second side. Find the sides of the rectangle, its S = 144 m2.

Given:

Rectangle;

Area – 144 m ^ 2;

The first side is? 2 m shorter than the doubled second;

The second side is? m.

Solution:

Find the sides of the rectangle using the equation. Let x m be the length of the second side. Then the first side of the rectangle, which is 2 m shorter than the doubled second side, is equal to (2x – 2) m.To construct the equation, we use the knowledge that the area of ​​the rectangle is 144 m ^ 2 and is calculated as the product of adjacent sides:

x (2x – 2) = 144;

2x ^ 2 – 2x – 144 = 0;

D = (-2) ^ 2 – 4 * 2 * (-144) = 1156;

x1 = (2 + √1156) / (2 * 2) = 9 (m) – the second side;

x2 = (2 – √1156) / (2 * 2) = -8 – the side cannot be negative;

2 * 9 – 2 = 16 (m) – the first side.

Answer: 9 and 16 m.