Question

If length of the diagonals of rhombus ABCD are 8 cm and 6 cm, then each of its sides is .

• A. 10 cm
• B. 5 cm
• C. 7 cm
• D. 4 cm

Answer 1

The correct option is B 5 cm

Since diagonals of the rhombus intersect at ${90}^{\circ }$ and they bisect each other we can find the length of the side using Pythagoras theorem.

If AC = 8 cm, BD = 6 cm, then OD = OB = 3 cm and OA = OC = 4 cm

In $△$ OBC,

${OB}^2$ + ${OC}^2$ = ${BC}^2$

$3^2$ + $4^2$ = ${BC}^2$

9 + 16 = ${BC}^2$

25 = ${BC}^2$

∴ BC = 5 cm
$\therefore$ Each side of the rhombus = 5cm.