Question

Answer the 15 one with proper steps

Answer 1

Perimeter of a quadrilateral is the sum of its four sides.

You are given 3 sides and the perimeter. So the fourth side can be found out by subtracting the sum of three sides from perimeter.
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$\text{Given three sides are:} \\ 3 {x}^{2} y + 4xyz - 12 \\ 12 {x}^{2} y + 7xyz + 50 \\ 15 {x}^{2} y + 3xyz - 7x$

$\text{perimeter} = 30 {x}^{2} y + 9xyz - 15x + 100$

$\text{Let the fourth side is M}$

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$\text{sum of four sides = Perimeter}\\ \\ 3 {x}^{2} y + 4xyz - 12\\ + 12 {x}^{2} y + 7xyz + 50 \\ +15 {x}^{2} y + 3xyz - 7x+M = 30 {x}^{2} y + 9xyz - 15x + 100\\ \\ 30 {x}^{2} y + 14xyz - 7x + 38 + M = 30 {x}^{2} y + 9xyz - 15x + 100\\ \\ M = 30 {x}^{2} y + 9xyz - 15x + 100 - (30 {x}^{2} y + 14xyz - 7x + 38)\\ \\ M = 30 {x}^{2} y + 9xyz - 15x + 100- 30 {x}^{2} y - 14xyz + 7x - 38\\ \\ M = -5xyz-8x+62\\ \\ \boxed{\textbf{Fourth side = -5xyz - 8x + 62} }$

Answer 2

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Perimeter of a quadrilateral is the sum of its four sides.

You are given 3 sides and the perimeter. So the fourth side can be found out by subtracting the sum of three sides from perimeter.

____________________________

$\text{Given three sides are:} \\ 3 {x}^{2} y + 4xyz - 12 \\ 12 {x}^{2} y + 7xyz + 50 \\ 15 {x}^{2} y + 3xyz - 7x$

$\text{perimeter} = 30 {x}^{2} y + 9xyz - 15x + 100$

$\text{Let the fourth side is M}$

____________________________

$\text{sum of four sides = Perimeter}\\ \\ 3 {x}^{2} y + 4xyz - 12\\ + 12 {x}^{2} y + 7xyz + 50 \\ +15 {x}^{2} y + 3xyz - 7x+M = 30 {x}^{2} y + 9xyz - 15x + 100\\ \\ 30 {x}^{2} y + 14xyz - 7x + 38 + M = 30 {x}^{2} y + 9xyz - 15x + 100\\ \\ M = 30 {x}^{2} y + 9xyz - 15x + 100 - (30 {x}^{2} y + 14xyz - 7x + 38)\\ \\ M = 30 {x}^{2} y + 9xyz - 15x + 100- 30 {x}^{2} y - 14xyz + 7x - 38\\ \\ M = -5xyz-8x+62\\ \\ \boxed{\textbf{Fourth side = -5xyz - 8x + 62} }$