Find the perimeter and area of a rectangle whose diagonal is 13 cm and the smaller side is 5 cm.

1. A, B, C, D – the vertices of the rectangle. AC – diagonal. CD is the smaller side.

2. Calculate the large side of the AD rectangle. The calculation is performed using the formula of the Pythagorean theorem:

AD = √AC² – CD² = √13² – 5² = √169 – 25 = √144 = 12 cm.

3. Calculate the perimeter (P) of the rectangle ABCD:

P = 12 x 2 + 5 x 2 = 34 cm.

4. Calculate the area (S) of the rectangle ABCD:

S = 12 x 5 = 60 cm².

Answer: the perimeter of the rectangle is 34 centimeters, the area is 60 centimeters².