Question

3.1 score: 15.9/17 answered: 16/17 question 17 a rectangle is 6 times as long as it is wide. if the area is 24 square feet, find its perimeter. question help: ebook written example

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ feet. Then the length $l = 6w$ feet.

Step2: Use area formula

The area formula of a rectangle is $A=l\times w$. Substitute $l = 6w$ and $A = 24$ into it, we get $24=6w\times w=6w^{2}$.

Step3: Solve for width

Divide both sides of the equation $6w^{2}=24$ by 6: $w^{2}=\frac{24}{6}=4$. Then take the square - root of both sides. Since width cannot be negative, $w = 2$ feet.

Step4: Find the length

Since $l = 6w$, when $w = 2$, $l=6\times2 = 12$ feet.

Step5: Calculate the perimeter

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 12$ and $w = 2$ into it: $P=2(12 + 2)=2\times14 = 28$ feet.

Answer:

28 feet