Question

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

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

Answer 1

The correct option is C 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.

Let us consider, 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 = ${BC}^2$

$\therefore$ BC = 5 cm
All the sides of a rhombus are equal.
$\therefore$ Each side of the rhombus = 5 cm.