The Perimeter of a triangle is $17 x + 5 y - 11 z$ m. If its two sides are $5 x + 3 y + z$ m and $4 x + y - 7 z$ m, find its third side.

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Solution

The perimeter of a triangle is the sum of all sides of a triangle.
Given the perimeter of the triangle $17 x + 5 y - 11 z$ m.
Step 1: Find the sum of two given sides.
$5 x + 3 y + z 4 x + y - 7 z9 x + 4 y - 6 z$
Hence, the sum of two sides of a triangle is $9 x + 4 y - 6 z$ m.
Step 2: Subtract the sum of two sides from the perimeter of a triangle
$17 x + 5 y - 11 z 9 x + 4 y - 6 z - - +8 x + y - 5 z____$ (changing the sign of each term)
Hence, the third side of a triangle is $8 x + y - 5 z$ m.

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