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:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}\thicklines\put(8,1){\line(1,0){3}}\put(8,1){\line(1,1){1.5}}\put(11,1){\line(-1,1){1.5}}\put(8,1){\line(1,1){1.5}}\put(11,1){\line(-1,1){1.5}}\put(8,1.8){\sf{5x cm}}\put(10.3,1.8){\sf{(4x + 3y - 9) cm}}\put(8.6,0.75){\sf{(6x - 2y + 2) cm}}\end{picture}$

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☯ Sides of equilateral triangle are equal :

↠ 5x = (4x + 3y – 9) = (6x – 2y + 2)

↠ 5x = (4x + 3y – 9)

↠ 5x – 4x = 3y – 9

↠ x = 3y – 9 ⠀— eq. ( I )

⠀

↠ 5x = (6x – 2y + 2)

↠ 2y – 2 = 6x – 5x

↠ 2y – 2 = x

• putting the value of x from eq. ( I )

↠ 2y – 2 = 3y – 9

↠ 9 – 2 = 3y – 2y

↠ y = 7

☯ Using value of y in eq. ( I ) :

↠ x = 3y – 9

↠ x = 3(7) – 9

↠ x = 21 – 9

↠ x = 12

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$\underline{\bf{\dag}\:\:\textsf{Perimeter of Equilateral Triangle :}}$

$\dashrightarrow\tt\:\:Perimeter=Sum\:of\:all\:Sides\\\\\\\dashrightarrow\tt\:\:Perimeter=5x+(4x + 3y-9)+(6x-2y + 2)\\\\\\\dashrightarrow\tt\:\:Perimeter=5(12)+[4(12) + 3(7)-9]+[6(12)-2(7) + 2]\\\\\\\dashrightarrow\tt\:\:Perimeter =60 \:cm + 60 \:cm + 60 \:cm\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Perimeter_{triangle} = 180 \:cm}}$

⠀

$\therefore\:\underline{\textsf{Perimeter of equilateral triangle is \textbf{180 cm}}}.$

Answer 2

Given:

sides of given equilateral triangle

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

To find :

values of x and y and perimeter of the triangle.

Answer:

Sides are equal in an equilateral triangle.

Therefore,

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

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

Also we have,

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

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

And,

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

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

From eq (1) and (2)

we will get,

=> y - 7 = 0

=> y = 7

Substituting this value in eq (1)

=> x - (2)(7) + 2 = 0

=> x - 14 + 2 = 0

=> x - 12 = 0

=> x = 12

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

Therefore,

Side = 5 × 12 = 60 cm

We know that perimeter of equilateral triangle = 3(side)

Thus,

Perimeter = (3 × 60) = 180 cm