Question

the area of a rombus is 24cm² and one of diagonals is 4 cm. its other diagonals measures​

Answer 1

Answer:

Are of rhombus=1/2×first diagonal ×second diagonal

24cm²=1/2×4×x

24=2x

2x=24

x=24/2

x=12

Answer 2

• The other diagonal of the rhombus (d₂) = 12 cm.

Given :

• The area of a rhombus = 24 cm².
• The one diagonal = 4 cm.

To Find :

• The other diagonal of the rhombus.

Solution :

We have to find the other diagonal of the rhombus.

Let,

The other diagonal of the rhombus be x.

Area of rhombus is given. So, we can use the formal of the area of the rhmobus.

We know that,

$\star \: \: \: \boxed{ \red{ \bf{ A = \dfrac{1}{2} \times d_{1} \times d_{2}}}}$

Where,

• A = area of the rhombus.
• d₁ = one diagonal of the rhombus.
• d₂ = other diagonal of the rhombus.

Given,

• A = 24 cm².
• d₁ = 4 cm.

Now, substitute both the given values in the formula of area of the rhombus.

$\bf \implies 24 \: {cm}^{2} = \dfrac{1}{ \not2} \times \not4 \: cm \times x \\ \\ \\ \bf \implies24 \: {cm}^{2} = 2 \: cm \times x\\ \\ \\\bf \implies \dfrac{ \not24}{ \not2} \: cm = x\\ \\ \\ \bf \implies 12 \: cm = x \\ \\ \\ \: \: \: \bf \therefore \: \: x = 12\: cm$

Hence,

The other diagonal of the rhombus (d₂) is 12 cm.

Verification :

We know that,

$\star \: \: \: \boxed{ \red{ \bf{ A = \dfrac{1}{2}\times d_{1} \times d_{2}}}}$

Where,

• A = area of the rhombus.
• d₁ = one diagonal of the rhombus.
• d₂ = other diagonal of the rhombus.

Now we have,

• A = 24 cm².
• d₁ = 4 cm.
• d₂ = 12 cm.

Now, substitute all the values in the formula.

$\bf \implies 24 \: {cm}^{2} = \dfrac{1}{ \not2} \times 4 \: cm \times \not12 \: cm \\ \\ \\ \bf \implies24\: {cm}^{2} = 4 \times 6 \: {cm}^{2} \\ \\ \\ \bf \implies 24 \: {cm}^{2} = 24 \: {cm}^{2} \\ \\ \\ \: \: \: \bf \therefore \: \: \: L.H.S. = R.H.S.$

Hence Verified !