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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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