Question

If the length of the sides of an equilateral triangle are (4x + 3y) units, [5x +3(y–1)] units and [6(x – 1) + 4(y – 1)] units, then the length of its side is
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Answer 1

the length of side is 24 unit for the given triangle

Answer 2

The length of the side of the given equilateral triangle will be 24 units.

Given,

Sides of an equilateral triangle:

(4x + 3y) units, [5x + 3(y – 1)] units, and [6(x – 1) + 4(y – 1)] units

To find,

Length of the side of this equilateral triangle.

Solution,

An equilateral triangle is one that has all of its sides equal.

Here, the sides of the given equilateral triangle are,

$(4x + 3y)$ units,

$[5x + 3(y - 1)]$ units,

$[6(x - 1) + 4(y -1)]$ units.

Since all sides will be equal.

$(4x + 3y)=[5x + 3(y - 1)]=[6(x - 1) + 4(y -1)]$

Now,

$(4x + 3y)=[5x + 3(y - 1)]$     ...(1)

$(4x + 3y)=[6(x - 1) + 4(y -1)]$     ...(2)

Simplifying (1),

$4x + 3y=5x + 3y - 3$

$\implies 4x -5x = - 3$

$\implies -x = - 3$

Or, x = 3.     ...(3)

Simplifying (2),

$4x + 3y=6x - 6+ 4y -4$

$\implies 4x -6x= 4y-3y -10$

$\implies -2x= y -10$

$\implies y=10-2x$     ...(4)

Now, from (3), we have, x = -3. Substituting in (4), we get,

$y=10-2(3)=10-6=4$

⇒ y = 4.

From the above values of x and y, we can determine the sides as follows.

It is given that,

$side = 4x + 3y$

$\implies side =4(3)+3(4) = 12+12=24$

⇒ side of the given equilateral triangle = 24 units.

Therefore, the length of the side of the given equilateral triangle will be 24 units.