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?
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
JU = 13 cm
So, the side length is 13 cm.