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The sides of an equilateral triangle are given by $x + 3 y$ ; $3 x + 2 y - 2$ and $4 x + \frac{1}{2} y + 1$ respectively. Find the lengths of the sides of the triangle.

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15

units each

17

units each

12

units each

11

units each

answer is A.

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Detailed Solution

Given an equilateral triangle with sides,

x + 3 y

;

3 x + 2 y - 2

and

4 x + \frac{1}{2} y + 1

.
Since it is an equilateral triangle, the lengths of the sides are equal.
So,

x + 3 y = 3 x + 2 y - 2 = 4 x + \frac{1}{2} y + 1

∴ x + 3 y = 3 x + 2 y - 2

∴ y = 2 x - 2

2 x - y = 2

……..(1)
Also,

4 x + \frac{1}{2} y + 1 = x + 3 y

∴ 8 x + y + 2 = 2 x + 6 y

6 x + 2 = 5 y

6 x - 5 y = - 2

.........(2)
Multiplying equation (1) by 5 we get,

10 x - 5 y = 10

..........(3)
Subtracting equation (2) from equation (3) we get,

10 x - 5 y - 6 x + 5 y = 10 + 2

4 x = 12

\Rightarrow x = 3

Substituting

x = 3

in equation (1),

∴ y = 2 x - 2

\Rightarrow y = 4

The length of one side of equilateral triangle =

x + 3 y

.
Side

= 3 + 3 (4)

Side

= 15

units
Therefore, option (1) is correct.

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The sides of an equilateral triangle are given by x+3y; 3x+2y-2 and 4x+12y+1 respectively. Find the lengths of the sides of the triangle.

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The sides of an equilateral triangle are given by $x + 3 y$ ; $3 x + 2 y - 2$ and $4 x + \frac{1}{2} y + 1$ respectively. Find the lengths of the sides of the triangle.