Quadrilateral ABCD is a rhombus whose diagonals AC and BD are 12 and 16, respectively

Quadrilateral ABCD is a rhombus whose diagonals AC and BD are 12 and 16, respectively. Find the side of the rhombus AB.

In a rhombus, all sides are equal. The diagonals of the rhombus are perpendicular. The intersection of the diagonals halves the diagonals. This means that the diagonals of this rhombus form 4 identical right-angled triangles with legs 6 and 8 (half of the diagonals), in which the side of the rhombus is the hypotenuse. Let’s find the hypotenuse according to the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse):

a² + b² = c²;

6² + 8² = c²;

36 + 64 = c²;

c² = 100;

c = √100;

c = 10 – the hypotenuse of the triangle and the side of the rhombus.

Answer: 10