The sides of an equilateral triangle are (x + 3y) cm, (3x + 2y − 2) cm and [4x + (y/2) + 1] cm. Find the length of each side.

Given, In an equilateral triangle, all three sides are equal. ∴ x + 3y = 3x + 2y - 2 = 4x + + 1 Solving L.H.S of the above equation, we get : ⇒ x + 3y = 3x + 2y - 2 ⇒ x - 3x + 3y - 2y = -2 ⇒ -2x + y = -2 ⇒ y = 2x - 2 .....(1) Solving R.H.S of the above equation, we get : Substituting value of y from equation (1) in (2), we get : ⇒ 3(2x - 2) - 2x = 6 ⇒ 6x - 6 - 2x = 6 ⇒ 4x - 6 = 6 ⇒ 4x = 6 + 6 ⇒ 4x = 12 ⇒ x = ⇒ x = 3. Substituting value of x in equation (1), we get : ⇒ y = 2(3) - 2 ⇒ y = 6 - 2 ⇒ y = 4. Substituting value of x and y in x + 3y, we get : ⇒ x + 3y = 3 + 3(4) = 3 + 12 = 15 cm. Since, all sides are equal. Hence, the length of each side is 15 cm.

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Solve the following system of equations by using the method of cross multiplication:
2x − 5y + 8 = 0, x − 4y + 7 = 0

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Solve the following system of equations by using the method of cross multiplication:
5x − 4y + 2 = 0, 2x + 3y = 13

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Mathematics

The sides of an equilateral triangle are (x + 3y) cm, (3x + 2y − 2) cm and [4x + (y/2) + 1] cm. Find the length of each side.

Linear Equations

Related Questions

Solve the following system of equations by using the method of cross multiplication:
2x − 5y + 8 = 0, x − 4y + 7 = 0

Solve the following system of equations by using the method of cross multiplication:
5x − 4y + 2 = 0, 2x + 3y = 13

Mathematics

The sides of an equilateral triangle are (x + 3y) cm, (3x + 2y − 2) cm and [4x + (y/2) + 1] cm. Find the length of each side.

Linear Equations

Related Questions

Solve the following system of equations by using the method of cross multiplication:2x − 5y + 8 = 0, x − 4y + 7 = 0

Solve the following system of equations by using the method of cross multiplication:5x − 4y + 2 = 0, 2x + 3y = 13

Solve the following system of equations by using the method of cross multiplication:
2x − 5y + 8 = 0, x − 4y + 7 = 0

Solve the following system of equations by using the method of cross multiplication:
5x − 4y + 2 = 0, 2x + 3y = 13