Question

1. if the length of a rectangle is 4 units more than its width and its total area is 20 square units, which is the standard form of the quadratic that represents the dimensions of the rectangle?

a. (w^{2}+4w = 20)
b. (0=(w + 4)w)
c. ((w + 5)(w - 4)=0)
d. (0=w^{2}+4w - 20)

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = w + 4$.

Step2: Use area formula

The area formula for a rectangle is $A=l\times w$. Given $A = 20$, we substitute $l$: $20=(w + 4)w$.

Step3: Expand and rearrange

Expand $(w + 4)w$ to get $w^{2}+4w$. Then rearrange to standard - form quadratic $0=w^{2}+4w - 20$.

Answer:

d. $0 = w^{2}+4w - 20$