The area of the rhombus is 96 and one of its diagonals is 16. Find the perimeter of the rhombus.

There are three known methods for determining the area of ​​a rhombus. One of the ways is when the area is found through half the product of the diagonals of the rhombus. Therefore, from the area formula, you can find the second diagonal:

S = d1 * d2 / 2;

d1 = 2 * S / d2; = 2 * 96/16 = 12;

Considering that the diagonals of the rhombus always intersect at right angles and at the same time divide each other in half, it can be argued that as a result of dividing by the diagonals, the rhombus forms four right-angled triangles, the legs of which are:

a = d1: 2 = 12: 2 = 6;

b = d2: 2 = 16: 2 = 8;

Therefore, you can find the side of the rhombus that is the hypotenuse using the Pythagorean theorem:

c ^ 2 = a ^ 2 + b ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100 = 10 ^ 2;

c = 10;

And since all sides of the rhombus are equal, the perimeter will be:

P = c + c + c + c = 4 * c = 4 * 10 = 40.