Question

a rectangular area is to be fenced in along a straight river bank as illustrated. the length of the fenced - in area is to be 5 feet greater than the width, and the total amount of fencing to be used is 95 feet. find the width and length of the fenced - in area. the width of the fenced - in area is

Explanation:

Step1: Define variables

Let the width of the fenced - in area be $w$ feet. Then the length $l$ is $w + 5$ feet. Since the area is along a river bank, the amount of fencing used is $2w+l$. Given that the amount of fencing is 95 feet, so $2w+(w + 5)=95$.

Step2: Solve the equation for $w$

Combine like - terms: $2w+w+5 = 95$, which simplifies to $3w+5 = 95$. Subtract 5 from both sides: $3w=95 - 5=90$. Divide both sides by 3: $w=\frac{90}{3}=30$ feet.

Step3: Find the length

Since $l=w + 5$, substitute $w = 30$ into the equation. Then $l=30 + 5=35$ feet.

Answer:

The width of the fenced - in area is 30 feet and the length is 35 feet.