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.
• B. Yes,12 cm.
• C. Yes, 13 cm.
• D. No, it is not possible.

Answer 1

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 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

${OJ}^2$+ ${OU}^2={JU}^2$

$5^2$+ ${12}^2={JU}^2$

$25+144={JU}^2$

$169={JU}^2$

JU = 13 cm

So, the side length is 13 cm.