One side of the rectangle is 5 cm larger than the other, and the diagonal

One side of the rectangle is 5 cm larger than the other, and the diagonal of the rectangle is 25 cm. Determine the lengths of the sides of the rectangle.

From the condition, we know that one side of the rectangle is 5 cm larger than the other, and the diagonal of the rectangle is 25 cm. To find the lengths of the sides of the rectangle, we use the Pythagorean theorem.

Since there are two sides and the diagonal is a right-angled triangle.

Let’s denote one of the sides by x cm, and the other by (x + 5) cm.

c ^ 2 = a ^ 2 + b ^ 2;

x ^ 2 + (x + 5) ^ 2 = 25 ^ 2;

x ^ 2 + x ^ 2 + 10x + 25 = 625;

2x ^ 2 + 10x – 600 = 0;

x ^ 2 + 5x – 300 = 0;

D = 25 + 1200 = 1225;

x1 = (-5 + 35) / 2 = 15 cm;

x2 = (-5 – 35) / 2 = -20 is not suitable.

So, 15 cm and 15 + 5 = 20 cm side lengths.