The perimeter of the rectangle is 26 cm and its area is 42 cm2, find the sides.

1. Vertices of a rectangle A, B, C, D.
2. Let’s designate the length of the AB side by the index “a”, the length of the AD side by the index “b”.
3. Let’s compose two equations:
(1) 2a + 2b = 26; a + b = 13; a = 13 – b;
(2) ab = 42;
4. Substitute the value a = (13 – c) from the first equation into the second:
(13 – c) b = 42;
13c – b² = 42;
в² – 13в + 42 = 0;
The first value in = (13 + √169 – 4 x 42) / 2 = (13 + 1) / 2 = 7 cm.
The second value is at = (13 – 1) / 2 = 6 cm.
The length of blood pressure can be 7 cm or 6 cm.
The first value is a = 13 – 7 = 6 cm.
The second value is a = 13 – 6 = 7 cm.
Answer: the length of the AB side can be 6 cm or 7 cm, the length of the BP side can be 7 cm or 6 cm.