the length of the fenced in area is to be 5 ft greater than the width and the total amount of fencing to be used is 89 ft find the width and length

Let's denote the width as \(w\) and the length as \(l\). The problem states that the length of the fenced area is 5 feet greater than the width: \[ l = w + 5 \] The total amount of fencing to be used is 89 feet, which includes both the length and the width: \[ 2w + 2l = 89 \] Now, substitute the expression for \(l\) from the first equation into the second equation: \[ 2w + 2(w + 5) = 89 \] Distribute and combine like terms: \[ 2w + 2w + 10 = 89 \] \[ 4w + 10 = 89 \] Subtract 10 from both sides: \[ 4w = 79 \] Divide by 4: \[ w = 19.75 \] Now that we have the width, we can find the length using the first equation: \[ l = w + 5 \] \[ l = 19.75 + 5 \] \[ l = 24.75 \] Therefore, the width is 19.75 feet and the length is 24.75 feet.