find the width

Question

John has a patio next to his house that is 15 ft by 10 ft. He wants to put a uniform flower bed around the patio. the area of the flower bed will be 100ft^2. Write an equation that can be used to find w, the width of the flower bed. Simplify your quadratic equation to standard form. I am confused, please explain step by step 

Answer 1

Hi Aisha,

 

The patio is 15ft by 10ft. So its a rectangle with width and length given. So area of the patio is 150 sq ft...........(1)

Now John wants to put a flower bed AROUND the patio. So imagine another rectangle bigger than the first such that there is a constant width between the 2 rectangles (I am unable to draw here but u can draw 2 rectangles one inside the other such that the gap between the 2 will represent the flower bed area.  )

 

Now if the width of the flower bed is say 'w' ft then as it goes around the patio, the new length and width of the patio PLUS the flower bed will be (15+2w)ft and (10+2w) ft  

( we add 2w to the length and width of patio as the flower bed goes around it)

 

So area of the flowerbed with patio inside is (15+2w)*(10+2w) sq ft .............(2)

 

Now given that area of flower bed is 100 ft. So the area of flower bed is the difference of equations (1) and (2)

 

(15+2w)*(10+2w) - 150 = 100

 

So need to solve this quadratic equation to get the answer.

 

Simplifying the equation we get 

 

150+30w+20w+4w² -150 = 100

 

Rearranging we get 

 

4w² + 50w -100 = 0

 

Dividing the equation by 2 through out we simplify as 

 

2w² +25w -50 =0

 

Solving the equation we get w =3.187 and -15.687

 

Since the width cannot be negative we take the required width of flower bed = 3.187