Question

Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.

Answer 1

ABCD is a rhombus.




Here, segment AC and segment BD are the diagonals of the rhombus ABCD.

l(AC) = 16 cm and l(BD) = 12 cm.

Diagonals of a rhombus are perpendicular bisectors of each other.

∴ m∠AOD = 90º

Also, l(OA) = $\frac{1}{2}$l(AC) = $\frac{1}{2}$ × 16 = 8 cm

l(OD) = $\frac{1}{2}$l(BD) = $\frac{1}{2}$ × 12 = 6 cm

In right ∆AOD,

l(AD)² = l(OA)² + l(OD)² (Pythagoras theorem)

⇒ l(AD)² = (8)² + (6)²

⇒ l(AD)² = 64 + 36 = 100

⇒ l(AD) = $\sqrt{100}$ = 10 cm

All sides of a rhombus are equal.

∴ Perimeter of the rhombus ABCD = 4 × Side of a rhombus = 4 × 10 = 40 cm

Thus, the side and perimeter of the rhombus are 10 cm and 40 cm, respectively.