Question

perimeter of a rhombus is 146 cm and one diagonal is 55 cm find the other diagonal and the area of Rhombus​

Answer 1

Since all the sides of a rhombus are equal, perimeter =4a where a is a side.

So 4a = 146 gives a = 36.5 cm.

Let the rhombus be ABCD and let the diagonal AC = 55 cm

We also know that the diagonals bisect each other at right angles. Hence if the diagonals AC and BD of the rhombus bisect each other at right angles at O, we have in the right angled triangle AOB, AO = 55/2 = 27.5 cm, AB = 36.5 cm.

So by Pythagoras theorem, OB^2 = AB^2 - AO^2 = (36.5)^2 - (27.5)^2 = 1332.25- 756.25 =576.

So OB = 24 cm so BD = 48 cm.

Answer 2

Solution:-

• Find the length of one side:

• Perimeter = 146 cm

• Length = Perimeter ÷ 4

• Length = 146 ÷ 4 = 36.5 cm

• Find 1/2 of the known diagonal:

=> 1/2 of the diagonal = 55 ÷ 2 = 27.5 cm

=> Find 1/2 of the other diagonal:

• Let 1/2 of the other diagonal be x

• a² + b² = c²

• x² + 27.5² = 36.5²

• x² = 36.5² - 27.5²

• x² = 576

• x = 24

Find the length of the other diagonal:

• 1/2 the length = 24 cm

• the length = 24 x 2 = 48 cm

• Answer: The length of the other parallel line is 48 cm

i hope it helps you