Please help me solve this problem for my alegbra homework.

Question

A security fence encloses a rectangular area on one side of a park in a city. Three sides of fencing are used, since the fourth side of the area is formed by a building. The enclosed area measures 2738 square feet. Exactly 148 feet of fencing is used to fence in three sides of this rectangle. What are the possible dimensions that could have been used to construct this area?

Answer 1

Let L = Length and W = Width of the rectangle.

 

LW = 2738

2W + L = 148 => L = 148 - 2W

 

Substitute:

(148 - 2W)W= 2738

 

Multiply and collect terms

2W² - 148W  + 2738 = 0

 

W² - 74W + 1359 = 0

The quadratic formula gives W = 37 and then L = 74

 

If I need to refresh you on the quadratic formula, please send me a message!

Answer 2

There will be an equation for the amount of fencing, an equation for the area and then use substitution

 

Let X = the width of the rectangular area

 

let Y = the length

 

X + X + Y = 148       This is the amount of fencing used

 

X·Y = 2738         This is the area

 

Y = 2738/X

 

now substitute

 

X + X + 2738/X = 148

 

2X + 2738/X = 148

 

multiply through by X and get terms on one side

 

2X² - 148X + 2738 = 0

 

X² - 74X + 1369 = 0

 

(X -37)(X - 37) = 0

 

X = 37

 

Y = 74 

 

Two sides of the fence are 37 feet and one side is 74 feet.