# The lengths of the sides of the rectangle are expressed in whole numbers. Find the largest side of the rectangle if you know

**The lengths of the sides of the rectangle are expressed in whole numbers. Find the largest side of the rectangle if you know that its area is 2015cm2 and the perimeter is less than 200cm.**

To solve this problem, we introduce two conditional variables “X” and “Y”, through which we denote the sides of the rectangle.

Then, based on the data of the problem, we compose the following equations:

1) (X + Y) x 2 = 200;

2) X x Y = 2015.

Solving a system of two equations with two unknowns, we get X = 100 -Y.

Substituting X in the second equation, we get the quadratic equation Y ^ 2 – 100Y + 2015 = 0.

Solving the quadratic equation, we get U1 = 28 cm and U2 = 72 cm.

Therefore, X1 = 100 – 28 = 72 cm, and X2 = 100 – 72 = 28 cm.

Answer: The large side of the rectangle is 72 cm.