Question

the area of a rhombus is 84 cm² and its length of one diagonal is 24cm² find the length of other diagonal and also side of rhombus​

Answer 1

Answer:

length of second diagonal =7

length of side = 11.47

may be it is right not sure

Answer 2

Required Answer:-

Given:

• The area of a rhombus is 84 cm² and it's length of one diagonal is 24 cm.

To Find:

• The length of other diagonal and the side of the rhombus.

Solution:

We have,

➡ Area = 84cm²

➡ d₁ = 24cm.

We know that,

➡ Area of Rhombus = ½ d₁ d₂ where d₁ and d₂ are the diagonals of the rhombus.

Here,

➡ d₁ = 24cm.

Therefore,

➡ ½ × 24 × d₂ = 84

➡ d₂ = 84/12

➡ d₂ = 7

★ Hence, the length of the other diagonal is 7 cm.

From the figure, AC and BD are the diagonals where AC = 7 cm and BD = 24 cm.

➡ AO = ½AC = 3.5 cm.

➡ BO = ½BD = 12 cm.

Here,

➡ ∠AOD = 90°

By Pythagoras Theorem,

➡ AD² = AO² + OD²

➡ AD² = (3.5)² + (12)²

➡ AD² = 12.25 + 144

➡ AD² = 156.25

➡ AD = √156.25 cm

➡ AD = 12.5 cm.

★ Hence, each side of the rhombus measures 12.5 cm.

Answer:

• Other diagonal of the rhombus measures 7 cm.
• Length of each side = 12.5 cm.