The diagonals of the rhombus are 3: 4, and the perimeter is 200 cm. Find the area of the rhombus.

We know from the condition that the diagonals of the rhombus are related as 3: 4, and we also know that the perimeter of the rhombus is 200 cm.

To calculate the area of ​​a rhombus, apply the formula S = 1/2 d1 * d2.

In order to calculate the length of the diagonals, we first of all find the length of the side of the rhombus. P = 4a;

a = P / 4 = 200/4 = 50 cm.

Let us introduce the coefficient of similarity k and write the diagonals as 3k and 4k.

The halves of the diagonals are related as whole in the same proportions.

Consider a right-angled triangle formed by the halves of the diagonals (they intersect at right angles) and the side of the rhombus, the hypotenuse.

50 ^ 2 = 9k ^ 2 + 16k ^ 2;

25k ^ 2 = 2500;

k ^ 2 = 100;

k = 10.

Diagonals 3 * 10 = 30 cm and 4 * 10 = 40 cm.

S = 1/2 * 30 * 40 = 120/2 = 60 cm ^ 2.