The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is :
3 cm
5 cm
7 cm
9 cm

Question

The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is : 1. 3 cm 2. 5 cm 3. 7 cm 4. 9 cm

KnowledgeBoat · Accepted Answer

Let AC = 6 cm and BD = 8 cm. We know that, Diagonals of rhombus are perpendicular and bisect each other, OB = BD = 4 cm and AO = AC = 3 cm. In right triangle AOB, By pythagoras theorem we get, Hypotenuse2 = Base2 + Height2 ⇒ AB2 = AO2 + OB2 ⇒ AB2 = 32 + 42 ⇒ AB2 = 9 + 16 ⇒ AB2 = 25 ⇒ AB = = 5 cm. ∴ The length of each side of the rhombus is 5 cm. Hence, option 2 is the correct option.

Mathematics

The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is :
3 cm
5 cm
7 cm
9 cm

Pythagoras Theorem

Related Questions

In the adjoining figure, AC =
17 cm
20 cm
22 cm
24 cm

The lengths of the diagonals of a rhombus are 5 cm and 12 cm. The length of each side of the rhombus is:
13 cm
6.5 cm
6.25 cm
5.25 cm

Mathematics

The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is :3 cm5 cm7 cm9 cm

Pythagoras Theorem

Related Questions

In the adjoining figure, AC =17 cm20 cm22 cm24 cm

The lengths of the diagonals of a rhombus are 5 cm and 12 cm. The length of each side of the rhombus is:13 cm6.5 cm6.25 cm5.25 cm

The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is :
3 cm
5 cm
7 cm
9 cm

In the adjoining figure, AC =
17 cm
20 cm
22 cm
24 cm

The lengths of the diagonals of a rhombus are 5 cm and 12 cm. The length of each side of the rhombus is:
13 cm
6.5 cm
6.25 cm
5.25 cm