In a rhombus with side √52, half of one diagonal is 4. Find the second diagonal of the rhombus.

Let’s take a look at one of four right-angled triangles formed by the side of a rhombus and half of the diagonals.

We know the hypotenuse of the triangle and it is equal to √52 units. and one of the legs is 4 units.

We can find the length of the second leg (which is half of the second diagonal of the rhombus) using the Pythagorean theorem.

Let’s remember her.

The square of the hypotenuse is equal to the sum of the squares of the legs:

c ^ 2 = a ^ 2 + b ^ 2;

We substitute the known values ​​into the formula and perform the calculations:

(√52) ^ 2 = 4 ^ 2 + b ^ 2;

52 – 16 = b ^ 2;

b ^ 2 = 36;

b = 6 units

So, half of the second diagonal is 6 units.

d2 = 2 * b = 2 * 6 = 12 units.

Answer: 12 units. Is the length of the second diagonal.