Can a kite be constructed if one of its side = 4.5 cm and diagonals length is 8.4 cm and 5.8 cm? What property of a kite is used in this construction?

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By definition, a kite is a quadrilateral that has two pairs of equal adjacent sides. It has a property that its diagonals are perpendicular, and the point of its intersection divides the shorter diagonal into equal parts. We'll use this property.

The shorter diagonal has length of `5.8 cm`...

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Hello!

By definition, a kite is a quadrilateral that has two pairs of equal adjacent sides. It has a property that its diagonals are perpendicular, and the point of its intersection divides the shorter diagonal into equal parts. We'll use this property.

The shorter diagonal has length of `5.8 cm` so its half is `2.9 cm.` From the right triangle `AOB` we obtain

`OB=sqrt(4.5^2-2.9^2) approx 3.44(cm).`

So to construct a kite draw a segment of the length `8.4 cm` (the longer diagonal), measure `3.44 cm` from one end, make a perpendicular at that point and measure `2.9 cm` at both sides.

If the length of a side would be less than `2.9cm,` such a kite would be impossible.

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