Question

clsie is planting a rectangular section of grass. if the perimeter of the rectangle is 96 feet, what are the length and width of the rectangular section? enter the correct answers in the boxes. length = feet width = feet

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $P$ is the perimeter, $l$ is the length and $w$ is the width. Here, $l=6x - 15$, $w = x$ and $P=96$. So, $96=2((6x - 15)+x)$.

Step2: Simplify the equation

First, simplify the right - hand side of the equation: $96 = 2(6x - 15+x)=2(7x - 15)$. Then, distribute the 2: $96=14x-30$.

Step3: Solve for x

Add 30 to both sides of the equation: $96 + 30=14x$, so $126 = 14x$. Divide both sides by 14: $x=\frac{126}{14}=9$.

Step4: Find length and width

The width $w=x = 9$ feet. The length $l=6x - 15$. Substitute $x = 9$ into the length formula: $l=6\times9-15=54 - 15=39$ feet.

Answer:

Length = 39 feet
Width = 9 feet