Question

If the perimeter of a rectangle is `5x^2+2xy-7y^2+16`, and the length is `-2x^2+6xy-y^2+15`, what is the width?

Answer 1

`rArrW=9/2x^2-5xy-5/2y^2-7`

Explanation:

Name `P` the perimeter of the rectangle.
Name `L` its length and `W` its width.

Given:
`P=5x^2+2xy-7y^2+16`

`L=-2x^2+6xy-y^2+15`

`P_(Rec)=2*(L+W)`

`rArr5x^2+2xy-7y^2+16=2*(-2x^2+6xy-y^2+15+W)`

`rArr5x^2+2xy-7y^2+16=-4x^2+12xy-2y^2+30+2W`

`rArr5x^2+2xy-7y^2+16+4x^2-12xy+2y^2-30=+2W`

`rArr5x^2+4x^2+2xy-12xy-7y^2+2y^2+16-30=+2W`

`rArr9x^2-10xy-5y^2-14=+2W`

`rArr(9x^2-10xy-5y^2-14)/2=W`

`rArr9/2x^2-5xy-5/2y^2-7=W`