Question

dain is planting a rectangular section of grass. if the perimeter of the rectangle is 98 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 perimeter, $l$ is length and $w$ is width. Here, $l=6x - 15$, $w = x$ and $P = 98$. So, $98=2((6x - 15)+x)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(6x - 15)+x=7x - 15$. Then the equation becomes $98 = 2(7x - 15)$. Distribute the 2: $98=14x-30$.

Step3: Solve for x

Add 30 to both sides of the equation: $98 + 30=14x-30 + 30$, which gives $128 = 14x$. Then divide both sides by 14: $x=\frac{128}{14}=\frac{64}{7}$.

Step4: Find length and width

Width $w=x=\frac{64}{7}$ feet. Length $l = 6x-15=6\times\frac{64}{7}-15=\frac{384}{7}-\frac{105}{7}=\frac{384 - 105}{7}=\frac{279}{7}$ feet.

Answer:

Length = $\frac{279}{7}$ feet, Width = $\frac{64}{7}$ feet