Question

A rectangular turf of size 20 feet by 30 feet is surrounded by a flower bed of uniform width

all around. The total area of the turf and the flower bed is 1200 sq.ft. What is the width of the

flower bed? Show your work algebraically.(4 points)

2) You are running a concession stand at a basketball game. You are selling hot dogs and

Answer 1

5 ft

Explanation:

Total area of turf and flower bed is
`1200\ \text{ft}^2`

Turf dimensions is 20 feet by 30 ft

Area of turf =
`20* 30=600\ \text{ft}^2`

Area of flower bed =
`1200-600=600\ \text{ft}^2`

Let
`x` be the width of the flower bed so area of flower bed is

`2* 30x+2(20+2x)x=600\\\Rightarrow 30x+20x+2x^2=300\\\Rightarrow 2x^2+50x-300=0\\\Rightarrow x^2+25x-150=0\\\Rightarrow x=(-25\pm √(25^2-4* \:1* \left(-150\right)))/(2* \:1)\\\Rightarrow x=5,-30`

So, width of the flower bed is 5 ft.