a patio in the shape of a rectangle, is fenced on all sides with 134 feet of fencing. the patio is 5 feet less wide than its long. what is the area of the patio?

The area of the patio is 1,116 ft^2

Step-by-step explanation:

Here in this question, we are interested in calculating the area of the patio.

Mathematically, area of patio is;

length * width

Unfortunately we do not have these values. Thus we need to get this from the value of the perimeter of the fencing and the relationship between the width and the length.

Mathematically, the total length of the fencing is the perimeter of the fencing.

Now, we are also told that the patio is 5 feet less wide than it is long.

So if the length is x ft, the width is (x-5) ft

Mathematically;

the perimeter of a rectangle is;

2(l + b)

Writing this in the x terms and equating to the perimeter, we have;

2( x + x -5) = 134

divide through by 2

2x -5 = 67

2x = 67 + 5

2x = 72

x = 72/2

x = 36 ft

Thus since the length is 36 ft, the width would be x -5 = 36 -5 = 31 ft

Done? No!

The question asks to calculate the area. Let’s move these values to the initial equation of the area in the start of the question.

Thus, we have 31 * 36 = 1,116 ft^2

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8