Question

Is it possible to construct a rhombus ABCD with AC = 24cm and BD = 10cm? If yes, find the length of the side of a rhombus.

• A. Yes, 11cm
• 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 AC = 24cm. Take the midpoint of line segment by ruler and mark it O.

Step 2: At O, draw a line perpendicular to AC. Along that line mark 5 cm above and 5 cm below.

Step 3: Mark the point 5 cm above point O as D and 5 cm below point O as B.

Step 4: Join all the points A, B, C and D.

So, it is possible to construct a rhombus if the length of its diagonals are known.

We know that diagonals of rhombus are perpendicular to each other and they bisect each other.

AC = 24cm

OA = OC = 12 cm

BD = 10 cm

OB = OD = 5 cm

OD${}^2$ +OC${}^2$ = DC${}^2$

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

25 + 144= DC${}^2$

169 = DC${}^2$

DC = 13cm

So, the side length is 13cm.