Question

find lengths using area and perimeter mastery check the perimeter of a rectangle is 22 feet, and the area is 18 square feet. what are its length and width? the length is feet. the width is feet. 3 4 9 11

Explanation:

Step1: Set up equations

Let the length be $l$ and the width be $w$. The perimeter formula is $P = 2(l + w)$, so $2(l + w)=22$, which simplifies to $l + w=11$, or $l = 11 - w$. The area formula is $A=lw$, so $lw = 18$.

Step2: Substitute and solve

Substitute $l = 11 - w$ into $lw = 18$, we get $(11 - w)w=18$. Expand to $11w-w^{2}=18$, or $w^{2}-11w + 18=0$. Factor the quadratic equation: $(w - 2)(w - 9)=0$. So $w = 2$ or $w = 9$.
If $w = 2$, then $l=11 - 2=9$. If $w = 9$, then $l=11 - 9 = 2$.

Answer:

The length is 9 feet. The width is 2 feet. (Or the length is 2 feet. The width is 9 feet.)