Find the side of the square that is equal in size to a rhombus with a side of 21 cm and a height of 14 cm.

Let’s draw the height BH in the rhombus ABCD. By the condition of the problem, BH = 14 cm, AB = 21 cm.

1) Find the area of the triangle ABD:

S (ABD) = 1/2 * AB * BH = 1/2 * 21 * 14 = 21 * 7 = 147 (cm ^ 2).

2) Draw a diagonal BD. The area of triangle BCD will be equal to the area of triangle ABD (since the diagonal BD divides the rhombus into two triangles of equal area), we find the area of the rhombus ABCD:

S (ABСD) = 147 * 2 = 294 (cm ^ 2).

3) Find the side of a square whose area is 294 cm ^ 2. The side of a square is equal to the square root of its area, in our case it is √294 = 7√6 cm.

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