The diagonals of the rhombus are in a ratio of 2: 3, its area is 75 m2. Find the smaller diagonal of the rhombus.

In order to calculate the area of a given rhombus, you need to find the product of two diagonals and divide by two:

S = (d1 * d1) / 2;

S = (AC * BD) / 2.

Since the diagonals AC and BD are related as 2: 3, we express them as:

2x – the length of the AC diagonal;

3x – the length of the diagonal BD;

(2x * 3x) / 2 = 75;

2x * 3x = 75 * 2;

6x ^ 2 = 150;

x ^ 2 = 150/6 = 25;

x = √25 = 5;

AC = 2 * 5 = 10 m;

ВD = 3 * 5 = 15 m.

Let’s check the correctness of our calculation:

S = (10 * 15) / 2 = 150/2 = 75 m2.

Answer: the length of the smaller AC diagonal is 10 m.