The perimeter of the rectangle is 34cm, and its diagonal is 13cm. Find the area of a rectangle.

1. A, B, C, D – the vertices of the rectangle. P is the perimeter. S – area.

2.P = 2 (AB + AD) = 34 centimeters.

AB + AD = 17 centimeters.

3. Let’s designate the AB side by the symbol “a”, the AD side by the symbol “b”.

4. We compose the equations:

a + b = 17;

a² + b² = 13² = 169;

5. We square both sides of the first equation:

(a + b) ² = 17²;

a² + 2av + b² = 289;

6. From the resulting equation, subtract the second equation:

a² + 2ab + b² – a²- b² = 120;

2av = 120;

ab = 120: 2 = 60.

S = ab = 60 centimeters².

Answer: S = 60 centimeters².