Answer :
Final answer:
To find the altitude of a rhombus with an area equal to a 16 m² square field and one diagonal of 2m, we calculate the other diagonal using the rhombus area formula. This reveals that the altitude of the rhombus is the same as the given shorter diagonal, which is 2m.
Explanation:
To determine the altitude of a rhombus when the area and one of its diagonals are known, we use the formula for the area of a rhombus: Area = (d1 x d2) / 2, where d1 and d2 are the lengths of the diagonals.
Firstly, the area of the given square field is calculated using the formula Area = side x side. Since each side of the square is 4 meters, the area is 4m x 4m = 16 m².
As the area of the rhombus is equal to the area of the square field (16 m²), and we know that one of its diagonals (d1) is 2 meters, we can find the other diagonal (d2) using the rhombus area formula. Substituting the known values, we get 16 m² = (2m x d2) / 2. Solving for d2 gives us d2 = 16 m.
The altitude (h) of the rhombus is the height corresponding to the base formed by either one of the diagonals when the rhombus is split into two congruent triangles. Using the longer diagonal as the base, the other diagonal acts as the height. Therefore, the altitude of the rhombus is the same as the shorter diagonal, which is 2m.
