Question

In a rhombus ABCD, AC=8cm and BD=6cm , then each side is

Answer 1

Answer:

Step-by-step explanation:AC=8cm

BD=6cm

These are the diagonals. And diagonals of a rhombus bisect each other. OA=4cm and OB =3cm.Take triangle AOB, OA^2+OB^2=AB^2

4^2+3^2=AB^2

16+9=AB^2

25=AB^2

Therefore, AB=5cm

Answer 2

Answer:

(Diagram given in attachment)

AC = 6 cm

⇒ AO + CO = 6

⇒ AO + AO = 6             [∵ AO = CO]

⇒ 2AO = 6

⇒ AO = 6 ÷ 2

⇒ AO = 3 cm

⇒ AO = CO = 3 cm

BD = 8 cm

⇒ BO + OD = 8

⇒ BO + BO = 8                [∵ BO = OD]

⇒ 2BO = 8

⇒ BO = 8 ÷ 2

⇒ BO = 4 cm

⇒ BO = OD = 4 cm

In ΔAOB,

By Pythagoras Theorem,

(AB)² = (AO)² + (BO)²

⇒ (AB)² = 3² + 4²

⇒ (AB)² = 9 + 16

⇒ (AB)² = 25

⇒ (AB) = √25

⇒ AB = ±5

Side cannot be negative

∴ Side of Rhombus = 5 cm

Now let's find the perimeter

Perimeter = 4(Side)

Perimeter = 4(5)

★ Perimeter = 20 cm ★