If the perimeter of a triangle is 10x + 12y, and two of the sides are 4x + 14y and 4x − 2y, which is the third side?
A. 2x + 2y
B. 2x
C. 3x + y
D. x + y

Respuesta :

Answer:

The third side is

B. [tex]2x[/tex]

Step-by-step explanation:

Given:

Perimeter of triangle = [tex]10x+12y[/tex]

Two sides of the triangle are :

1) [tex]4x+14y[/tex]

2) [tex]4x-2y[/tex]

To find the third side.

Solution:

Let the third side be = [tex]z[/tex]

The perimeter can be given as sum of all 3 sides :

[tex]4x+14y+4x-2y+z[/tex]

Combining like terms.

[tex]4x+4x+14y-2y+z[/tex]

[tex]8x+12y+z[/tex]

The perimeter given = [tex]10x+12y[/tex]

So, we have:

[tex]8x+12y+z=10x+12y[/tex]

Solving for [tex]z[/tex]

Subtracting both sides by [tex]8x[/tex]

[tex]8x-8x+12y+z=10x-8x+12y[/tex]

[tex]12y+z=2x+12y[/tex]

Subtracting both sides by [tex]12y[/tex]

[tex]12y-12y+z=2x+12y-12y[/tex]

∴ [tex]z=2x[/tex]

Thus, the third side is = [tex]2x[/tex]

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