One side of a right-angled triangle is 9cm larger than the other. find the sides of a rectangle if its area is 112cm2.

1. Let’s denote one side of the rectangle through x cm.

2. Determine the length of the second side of the rectangle:

(x + 9) cm.

3. Let’s compose and solve the equation:

x * (x + 9) = 112;

x * x + x * 9 = 112;

x ^ 2 + 9x – 112 = 0;

D = 9 ^ 2 – 4 * 1 * (-112) = 81 + 448 = 529;

x1 = (-9 + 23) / (2 * 1) = 14/2 = 7;

x2 = (-9 – 23) / (2 * 1) = -32 / 2 = -16;

-16 – does not meet the condition of the problem.

4. One side of the rectangle is x = 7 cm.

5. What is the second side of the rectangle?

x + 9 = 7 + 9 = 16 cm.

Answer: the sides of the rectangle are 7 cm and 16 cm.