Question

The area of rhombus is 384 m2 and one of its diagonals is 24 m . what is the perimeter of the rhombus​

Answer 1

Answer:

The area of rhombus is 384 m2

find the perimeter of rhombus

One diagonal is 24m

Step-by-step explanation:

The area of rhombus

=>1/2*product of diagonal

substitute the value

=>384=1/2*product of diagonal

=>384=1/2*AC*BD

=>384=1/2*24*BD

=>BC=32

The pythogoras theorem using

one diagonal is =24/2=12

another diagonal is=32/2=16

AO^2+BO^2=AB^2

√16^2+√12^2=20m

The one side of rhombus is 20m

The perimeter is rhombus is

4a =4(20) =80m

the perimeter of rhombus is 80m

Answer 2

$\Large{\underbrace{\sf{\pink{Required\:Solution:}}}}$

Given thαt,

• The αreα of rhombus is 384 m².
• One of its diαgonαl is 24m.

◾️We need to find the perimeter of the rhombus.

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★$\large{\boxed{\sf{\pink{Area_{(rhombus)} = \dfrac{1}{2} \times d_1 \times d_2}}}}$

• Substitute the vαlues.

$\displaystyle{\sf{ 384m^{2}=\dfrac{1}{2} \times 24m \times d_2}}$

• Cαncel out 2 αnd 24.

$\displaystyle{\sf{ 384m^{2}=\dfrac{1}{\cancel{2}} \times \cancel{24m} \times d_2}}$

$\displaystyle{\sf{384m^{2}= 12m \times d_2}}$

• Transpose 12m to L.H.S.

$\displaystyle{\sf{ \dfrac{384m^{2}}{12m} = d_2}}$

• Cancel out this.

$\displaystyle{\sf{ d_2 = \dfrac{\cancel{384m^{2}}}{\cancel{12m}}}}$

$\large{\underline{\sf{\pink{d_2 = 32m}}}}$

Hence, the other diαgonαl is 32m.

_______________

So we hαve to find the side of the rhombus first.

We know thαt, diαgonαl bisect eαch other αt 90°.

so, Here we'll use Pythαgorαs Theorem.

★$\large{\boxed{\sf{\pink{(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}}}}}$

• Substitute the values.

$\implies{\sf{ (OA)^{2}+(OB)^{2}=(AB)^{2}}}$

$\implies{\sf{ \bigg( \dfrac{32}{2} \bigg)^{2} + \bigg( \dfrac{24}{2} \bigg)^{2} = (AB)^{2}}}$

$\implies{\sf{ (16)^{2} + (12)^{2} = (AB)^{2}}}$

$\implies{\sf{ 256+144= (AB)^{2}}}$

$\implies{\sf{ 400= (AB)^{2}}}$

$\implies{\sf{ \sqrt{400} = (AB)}}$

$\large\implies{\underline{\sf{\pink{AB = 20m}}}}$

Hence, the side is 20m.

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★$\large{\boxed{\sf{\pink{Perimeter_{(rhombus)}= 4(side)}}}}$

• Substitute the values.

$\implies{\sf{ 4(20) }}$

$\large{\boxed{\sf{\pink{80m}}}}$

Hence, the perimeter is 80m.

And we are done! :D

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