Question

The rectangle below has an area of y^4+11y^2+30 square meters and a length of y^2+5 meters. What represents the width of the rectangle?

Answer 1

Answer:

$y^2+6\ m$

Step-by-step explanation:

First factor the expression $y^4+11y^2+30:$

$y^4+11y^2+30=y^4+5y^2+6y^2+30=y^2(y^2+5)+6(y^2+5)=(y^2+5)(y^2+6).$

Use the formula

$A_{\text{rectangle}}=\text{width}\cdot \text{length}$

for finding the area of the rectangle.

If the length of the rectangle is $y^2+5$ meters, then its width is

$\text{width}=\dfrac{A_{\text{rectangle}}}{\text{length}}=\dfrac{y^4+11y^2+30}{y^2+5}=\dfrac{(y^2+5)(y^2+6)}{y^2+5}=y^2+6\ m.$