# Vanessa has 180 feet of fencing that she intends to use to build a rectangular play area for her dog. She wants the play area to enclose at least 1800 square feet. What are the possible widths of the play area?

##### 2 Answers

The possible widths of the play area are : 30 ft. or 60 ft.

#### Explanation:

Let length be

Perimeter =

and

Area =

From (1),

Substitute this value of

Solving this quadratic equation we have :

The possible widths of the play area are : 30 ft. or 60 ft.

#### Explanation:

#"using the following formulae related to rectangles"#

#"where "l" is the length and "w" the width"#

#• " perimeter (P) "=2l+2w#

#• " area (A) "=lxxw=lw#

#"the perimeter will be "180" feet "larrcolor(blue)"fencing"#

#"obtaining "l" in terms of "w#

#rArr2l+2w=180#

#rArr2l=180-2w#

#rArrl=1/2(180-2w)=90-w#

#A=lw=w(90-w)=1800#

#rArrw^2-90w+1800=0larrcolor(blue)"quadratic equation"#

#"the factors of + 1800 which sum to - 90 are - 30 and - 60"#

#rArr(w-30)(w-60)=0#

#"equate each factor to zero and solve for "w#

#w-30=0rArrw=30#

#w-60=0rArrw=60#