In the rectangle ABCD, the diagonal BD is 10cm. The distance from vertex C to BD is 4cm. Find the perimeter of ABCD.

1. CE – perpendicular to HP. P is the perimeter.

2. Let’s designate BE by the symbol “a”, DE by the symbol “in”.

3. Let’s compose two equations:

a + b = 10; a = 10 – b;

a x in = 4² = 16;

4. (10 – in) x in = 16:

b² – 10b + 16 = 0;

The first value in = (10 + √100 – 64) = (10 + 6) / 2 = 8.

The second value in = (10 – 6) / 2 = 2.

4. DE = 8 cm or 2 cm.

BE also has two meanings:

BE = 2 cm or 8 cm.

5. BC = √8² + 4² = √80 = 4√5 cm or BC = √2² + 4² = √20 = 2√5 cm.

6.СD = 2√5 cm or 4√5 cm.

7.P = 2 (2√5 + 4√5) = 12√5 cm.