Answer:
[tex]3x^2+xy-25=0[/tex]
Step-by-step explanation:
The length of the rectangle is:
[tex]L=x\cdot \sqrt{100}=x\cdot 10=10 x[/tex]
The width of the rectangle is:
[tex]W=\frac{1}{2}y+\frac{3}{2}x[/tex]
The area of the rectangle, which is the product between length and width, is equal to 125 cm^2:
[tex]A=L\cdot W=125[/tex]
Substituting the expressions for L and W found before, we get:
[tex](10x)(\frac{1}{2}y+\frac{3}{2}x)=125\\(10x)(y+3x)=250\\10xy+30x^2=250\\3x^2+xy-25=0[/tex]
