Question

“The sides of an equilateral triangle are given as 5x cm,(4x+3y-9)cm and(6x-2y+2)cm.Find the value of x and y and hence calculate the perimeter of the triangle”

Answer 1

Answer:

$\large\boxed{\sf{x=12,\;\;y = 7}}$

$\large\boxed{\sf{Perimeter=180\;cm}}$

Step-by-step explanation:

Given the sides of an equilateral triangle,

• (5x) cm
• (4x + 3y - 9) cm
• (6x - 2y + 2) cm

We know that, sides of an equilateral triangle are equal.

Therefore, we will get,

=> 5x = 4x + 3y - 9

=> x - 3y + 9 = 0 ........(1)

Also, we have,

=> 5x = 6x - 2y + 2

=> x - 2y + 2 = 0 ........(2)

Fhrthery, we have,

=> 4x + 3y - 9 = 6x - 2y + 2

=> 2x - 5y + 11 = 0 .......(3)

Now, solving eqn (1) and (2), we get,

=> y - 7 = 0

=> y = 7

Substituting this value in eqn (1), we get,

=> x - (2×7) + 2 = 0

=> x - 14 + 2 = 0

=> x - 12 = 0

=> x = 12

But, it's given that, side of equilateral triangle is 5x.

Therefore, we will get,

=> Side length = 5 × 12 = 60 cm

Hence, Perimeter = (3 × 60) = 180 cm

Answer 2

$\huge \underline {\underline \bold{ GIVEN :} }$

Sides of an equilateral triangle are :

• 5x cm
• (4x + 3y - 9)cm
• (6x-2y+2) cm

$\huge \underline {\underline \bold{ To \: Find : \:} } \:$

• the value of x and y
• the perimeter of the triangle

$\huge \underline {\underline \bold{ Solution :} }$

Firstly , we have to find the value of x and y

Therefore,

$\sf \: 5x = 4x + 3y - 9 \\ \sf x - 3y + 9 = 0......(1) \\ \\ \bold{ \: again \: } \\ \sf 5x = 6x - 2y + 2 \\ \sf x - 2 + 2y + 2 = 0.......(2) \\ \\ \sf \bold{we \: \: \: have} \\ \\ \sf4x + 3y - 9 = 6x - 2y + 2 \\ \sf2x - 5y + 11 = 0.....(3) \\ \\ \bold{solving \: eq \: (1) \: and \: eq \: (2)} \\ \\ \sf \: y - 7 = 0 \\ \sf \: y = 7 \\ \bold{ Substituting \: this \: value \: in \: eqn (1), we \: get,} \\ \sf \: x - (2 \times 7) + 2 = 0 \\ \sf x - 14 + 2 = 0 \\ \sf \: x - 12 = 0 \\ \sf \: x = 12 \\ \\ \bold {hence \: the \: value \: of} \bold \red{ \: x \: is \: 12 \: cm \: and \: y \: is \: 7cm }\:$

Now finding the side length :

$\bold {side \: length \bold \green{ = 5 \times 12cm \: = 60cm}}$

Now , lastly finding the perimeter :

$\bold{perimeter} = \bold \pink{(3 \times 60)cm \: = \: 180cm}$