Answer:
[tex]y^2+6\ m[/tex]
Step-by-step explanation:
First factor the expression [tex]y^4+11y^2+30:[/tex]
[tex]y^4+11y^2+30=y^4+5y^2+6y^2+30=y^2(y^2+5)+6(y^2+5)=(y^2+5)(y^2+6).[/tex]
Use the formula
[tex]A_{\text{rectangle}}=\text{width}\cdot \text{length}[/tex]
for finding the area of the rectangle.
If the length of the rectangle is [tex]y^2+5[/tex] meters, then its width is
[tex]\text{width}=\dfrac{A_{\text{rectangle}}}{\text{length}}=\dfrac{y^4+11y^2+30}{y^2+5}=\dfrac{(y^2+5)(y^2+6)}{y^2+5}=y^2+6\ m.[/tex]
