Question

If two consecutive sides of a rhombus are represented by 3x-6 and x+14 , then the perimeter of rhombus is​

Answer 1

Answer :

• Perimeter of rhombus is 96.

Given :

• If two consecutive sides of a rhombus are represented by 3x - 6 and x + 14

To find :

• Perimeter of rhombus

Solution :

We know that, In a rhombus all sides are equal so ,

According to question :

➟ 3x - 6 = x + 14

➟ 2x = 20

➟ x = 20/2

➟ x = 10

Now, putting the value of x = 10 in x + 4 to find the sides

➟ x + 14

➟ 10 + 24

➟ 24

Sides is 24.

Finding the perimeter of rhombus :

We know that

• Perimeter of rhombus = 4 × a

Where, a is side

➟ Perimeter of rhombus = 4 × a

➟ Perimeter of rhombus = 4 × 24

➟ Perimeter of rhombus = 96

Hence, Perimeter of rhombus is 96.

Verification :

➟ 3x - 6 = x + 14

➟ 3(10) - 6 = 10 + 14

➟ 30 - 6 = 24

➟ 24 = 24

Hence , Verified

Answer 2

$\large \tt \color{skyblue}{ \underline{Givᥱn : }}$

• If two consecutive sides of rhombus are represented by 3x - 6 and x + 14

$\large \tt \color{skyblue}{ \underline{To \: find : }}$

• Find the perimeter of rhombus

$\large \tt \color{skyblue}{ \underline{Soᥣᥙtion : }}$

$\sf{Wᥱ \: knoᥕ \: thᥲt \: ᥲᥣᥣ \: sidᥱ \: of \: rhombᥙs \: ᥲrᥱ \: ᥱqᥙᥲᥣ}$

$\sf{ \therefore \: 3x - 6 = x + 14}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \rightarrow \: 3x - x = 14 + 6}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \rightarrow \: 2x = 20}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \rightarrow \: x = \cancel \frac{20}{2} }$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \rightarrow \: x = 10}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \: \: \: \: \: \: \: \: \: \: \: ━━━━━━━━━━━━━━━━━━$

$\sf{side = 3x - 6 = 3 \times 10 - 6 = 24}$

$\fbox{ \sf{ \underline \pink{perimeter \: of \: rhombus = 4 x side}}}$

$\sf{ perimeter = 4 \times 24}$

$\sf{perimeter = 96}$

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore { \underline{Hence \: perimeter \: of \: rhombus \: is \: 96}}}$