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

Perimeter of a triangle is the sum of its all sides.
Here sides of two triangles are $(5 x + 3 y + z)$ and $(4 x + y - 7 z)$
Let third side is $A$ m.
$(5 x + 3 y + z)$ $+$ $(4 x + y - 7 z)$ $+$ $A$ $=$ Perimeter
$5 x + 3 y + z + 4 x + y - 7 z + A = 17 x + 5 y - 11 z$
$9 x + 4 y - 6 z + A = 17 x + 5 y - 11 z A = 17 x + 5 y - 11 z - 9 x - 4 y + 6 z = 8 x + y - 5 z$
Hence, the third side is $8 x + y - 5 z .$

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