Question

The length of a side of a square field is 4 m. What will be the altitude of a rhombus whose area is equal to the square field and one of its diagnols is 2m long?
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Answer 1

Area of the square field = (4 * 4) sq metres = 16 sq metres.

Area of the rhombus = 16 sq metres.

One diagonal of the rhombus = 2 metres

Let, the other diagonal of the rhombus be x metres.

Area of the rhombus = {(x * 2) / 2} sq metres = x sq metres.

So, x = 16.

Therefore, diagonals of the rhombus are of 2 metres and 16 metres; and they are perpendicular bisectors of one another.

Each side of the rhombus = √{(1^2) + (8^2)} metres = √65 metres.

Altitude of the rhombus = (16 / √65) metres