Question

find lengths using area and perimeter mastery check
a rectangle has an area of 30 square meters and a perimeter of 22 meters. what are its length and width?
the length is
the width is
6
8
11
15

Explanation:

Step1: Set up equations

Let the length be $l$ and the width be $w$. The area formula is $A = lw$, so $lw=30$. The perimeter formula is $P = 2(l + w)$, so $2(l + w)=22$, which simplifies to $l + w=11$, and $l=11 - w$.

Step2: Substitute and solve

Substitute $l = 11 - w$ into $lw = 30$: $(11 - w)w=30$. Expand to get $11w-w^{2}=30$, or $w^{2}-11w + 30=0$. Factor the quadratic equation: $(w - 5)(w - 6)=0$. So $w = 5$ or $w = 6$.
If $w = 5$, then $l=11 - 5=6$. If $w = 6$, then $l=11 - 6 = 5$.

Answer:

The length is 6 meters. The width is 5 meters.