Question

# Is it possible to construct a rhombus AJUN with AU = 24 cm and JN = 10 cm? If yes, what is the length of the side of the rhombus?

A

Yes, 11 cm

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B

Yes 12 cm

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C

Yes 13 cm

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D

No, it is not possible

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Solution

## The correct option is C Yes 13 cm Step 1: Draw AU = 24 cm. Take the midpoint of line segment by ruler and mark it O. Step 2: At O, draw a line perpendicular to AU. Along with that line mark 5 cm above and 5 cm below. Step 3: Mark the point 5 cm above point O as N and 5 cm below point O as J. Step 4: Join all the points A, J, U and N. So, it is possible to construct a rhombus if the length of its diagonals is known. We know that diagonals of a rhombus are perpendicular to each other and they bisect each other. AU = 24 cm OA = OU = 12 cm JN = 10 cm OJ = ON = 5 cm OJ2+ OU2=JU2 52+ 122=JU2 25+144=JU2 169=JU2 JU = 13 cm So, the side length is 13 cm.

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