Given a rectangle ABCD, the perimeter of which = 14cm. Side AB = 3cm. Find the length of the diagonal AC.

The AC diagonal divides the ABCD rectangle into two right-angled triangles – ABC and BCD, where AC is their common hypotenuse. We find the hypotenuse by the Pythagorean theorem:

AC² = AB² + BC²;

AC = √ (AB² + BC²).

Find the side of the rectangle BC if the perimeter is 14 cm:

2 * 3 + 2 * BC = 14;

2 * BC = 8;

BC = 4 cm.

Let’s find the hypotenuse, it is also the diagonal of the rectangle:

AC = √ (3² + 4²);

AC = √25;

AC = 5 cm.

Answer: The length of the AC diagonal is 5 cm.