Question

Lengths of the diagonal AC and diagonal BD of a rhombus are 6cm and 8cm respectively, find the lengths of each side of the rhombus.

Answer 1

Let $\square$ABCD be a rhombus whose lengths of diagonals AC and BD are 6 cm and 8 cm respectively ..



We know that the diagonals of a rhombus bisect each other at right angles.
Thus, we get:
OA = $\frac{1}{2}$ × AC
= $\frac{1}{2}$ × 6
= 3 cm
OB = $\frac{1}{2}$ × BD
= $\frac{1}{2}$ × 8
= 4 cm
Now, in right-angled triangle OAB, we have:
AB² = OA² + OB²
$\Rightarrow$AB² = (3)² + (4)²
$\Rightarrow$AB² = 9 + 16
$\Rightarrow$AB²= 25
$\Rightarrow$AB² = (5)²
On taking square roots of both sides, we get:
AB = 5 cm
Thus, the length of each side of the rhombus is 5 cm.