The perimeter of the rectangle is 26 cm, the area is 36 cm. Find the lengths of the sides of the rectangle.

From the problem statement, we know that the perimeter of the rectangle is 26 centimeters, and the area of ​​the same rectangle is 36 centimeters.

We know that the perimeter and area of ​​a rectangle can be found based on the formula:

P = 2 (a + b)
S = ab

Where
a – the length of the rectangle;
b is the width of the rectangle.

That is, we get that:

2 (a + b) = 26
ab = 36

Thus, we get a system of equations. Let us express a from the first equation and substitute it into the second:

a + b = 26/2
a + b = 13
a = 13-b

Then:

(13-b) b = 36
13b-b ^ 2 = 36
b ^ 2-13b + 36 = 0

D = (- 13) ^ 2-4 * 1 * 36 = 169-144 ° 25

√D = 5

b1 = (- (- 13) +5) / 2 * 1 = (13 + 5) / 2 = 18/2 = 9
b2 = (- (- 13) -5) / 2 * 1 = (13-5) / 2 = 8/2 = 4

Then:

a1 = 13-b1 = 13-9 = 4
a2 = 13-b2 = 13-4 = 9

That is, the sides of the rectangle are 9 and 4 centimeters