Question

Area of a rhombus is 96sqcm one of the diagonal is 12cm find the length of its side

Answer 1

Given:

A rhombus with

• Diagonal = D1 = 12 cm
• Area = 96 sq.cm

What To Find:

We have to find the length of rhombus.

How To Find:

To find the length, we will

• Find D2 (other diagonal) using a formula (F1)
• Length using a formula (F2)

Formula:

F1 = $\sf{Area = \dfrac{1}{2} \times D1 \times D2}$

F2 = $\sf{side = \dfrac{\sqrt{D1^2 + D2^2}}{2}}$

Solution:

• Finding D2.

Using the formula,

⇒ $\sf{Area = \dfrac{1}{2} \times D1 \times D2}$

Substitute the values,

⇒ $\sf{96 = \dfrac{1}{2} \times 12 \times D2}$

Cancel 2 and 12,

⇒ 96 = 6 × D2

Take 6 to LHS,

⇒ $\sf{\dfrac{96}{6} = D2}$

Divide 96 by 6,

⇒ 16 cm = D2

• Finding the length

Using the formula,

⇒ $\sf{side = \dfrac{\sqrt{D1^2 + D2^2}}{2}}$

Substitute the values,

⇒ $\sf{side = \dfrac{\sqrt{12^2 + 16^2}}{2}}$

Find the square,

⇒ $\sf{side = \dfrac{\sqrt{144 + 256}}{2}}$

Add,

⇒ $\sf{side = \dfrac{\sqrt{400}}{2}}$

Find the square root of 400,

⇒ $\sf{side = \dfrac{20}{2}}$

Divide 20 by 2,

⇒ side = 10 m

∴ Thus, side of rhombus is length is 10 m.