Question

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

Answer 1

The third side is

B.
`2x`

Explanation:

Given:

Perimeter of triangle =
`10x+12y`

Two sides of the triangle are :

1)
`4x+14y`

2)
`4x-2y`

To find the third side.

Solution:

Let the third side be =
`z`

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

`4x+14y+4x-2y+z`

Combining like terms.

`4x+4x+14y-2y+z`

`8x+12y+z`

The perimeter given =
`10x+12y`

So, we have:

`8x+12y+z=10x+12y`

Solving for
`z`

Subtracting both sides by
`8x`

`8x-8x+12y+z=10x-8x+12y`

`12y+z=2x+12y`

Subtracting both sides by
`12y`

`12y-12y+z=2x+12y-12y`

∴
`z=2x`

Thus, the third side is =
`2x`