Question

The lengths of the diagonals PR and QS of a rhombus are 20cm and 48 cm. respectively, find the length of each side of the rhombus.

Answer 1

Let $\square$PQRS be a rhombus whose diagonals are PR = 20 cm and QS = 48 cm.

We know that the diagonals of a rhombus bisect each other at right angles.
Thus, we have:
OP = $\frac{1}{2}$ × PR
= $\frac{1}{2}$ × 20
= 10 cm
OQ = $\frac{1}{2}$ × QS
= $\frac{1}{2}$ × 48
= 24 cm
Now, in right-angled triangle QOP, we have:
PQ² = OP² + OQ²
$\Rightarrow$ PQ² = (10)² + (24)²
$\Rightarrow$ PQ² = 100 + 576
$\Rightarrow$ PQ² = 676
$\Rightarrow$ PQ² = (26)²
On taking square roots of both sides, we get:
PQ = 26 cm
All sides of a rhombus are equal.
Thus, the length of each side of the rhombus is 26 cm.