The rectangle has a perimeter of 50 and an area of 156. Find the larger side of the rectangle.

Let the length of one and the sides of the rectangle be equal to X cm, and the length of its second side is equal to Y cm.

Then, by condition:

P = 2 * (X + Y) = 50 cm.

S = X * Y = 156 cm2.

Let us solve the system of two equations by the substitution method.

X + Y = 25.

X = 25 – Y.

(25 – Y) * Y = 156.

25 * Y – Y ^ 2 = 156.

Y ^ 2 – 25 * Y + 156 = 0.

Let’s solve the quadratic equation.

Y1 = 12 cm.

Y2 = 13 cm.

Then X1 = 25 – 12 = 13 cm.

X2 = 25 – 13 = 12 cm.

Answer: The large side of the rectangle is 13 cm.