Question

a rectangular area is to be fenced in along a straight river bank as illustrated. the total amount of fencing to be used is 96 feet. find the width and length of the fenced - in area. the length of the fenced - in area is to be 6 feet greater than the width, and the width of the fenced - in area is

Explanation:

Step1: Define variables

Let the width of the fenced - in area be $w$ feet and the length be $l$ feet. Since one side of the rectangle is along the river, the amount of fencing used is $2w + l=96$. Also, $l=w + 6$.

Step2: Substitute $l$ into the fencing equation

Substitute $l = w + 6$ into $2w + l=96$. We get $2w+(w + 6)=96$.

Step3: Simplify the equation

Combine like - terms: $2w+w+6 = 96$, which simplifies to $3w+6 = 96$.

Step4: Solve for $w$

Subtract 6 from both sides: $3w=96 - 6=90$. Then divide both sides by 3: $w=\frac{90}{3}=30$ feet.

Step5: Solve for $l$

Substitute $w = 30$ into $l=w + 6$. So $l=30 + 6=36$ feet.

Answer:

The width of the fenced - in area is 30 feet and the length is 36 feet.