Question

Bob wants to plant a 7 foot by 10 foot garden with a uniform border of petunias around the outside and still have 28 square feet to plant tomatoes and roses in the middle. How wide should the border of petunias be?

Answer 1

Width of the border is 1.5 feet.

Explanation:

Let x be the width ( in feet ) of the border,

Given,

The dimension of the garden = 7 foot by 10 foot,

So, the dimension of the middle ( garden area excluded border )= (7 - 2x) foot by (10 - 2x) foot

Hence, the area of the middle = (7 - 2x)(10 - 2x)

According to the question,

`(7 - 2x)(10 - 2x)=28`

`70 -14x-20x + 4x^2=28`

`4x^2 -34x+70-28=0`

`4x^2 -34x+42=0` ( Combine like terms )

`4x^2-(28+6)x+42=0` ( Middle term splitting )

`4x^2-28x-6x+42=0`

`4x(x-7)-6(x-7)=0`

`(4x-6)(x-7)=0`

By zero product property,

4x - 6 or x - 7 = 0

⇒ x = 1.5 or x = 7

Since, width of the border can not be equal to the dimension of the garden,

Therefore, the width would be 1.5 foot.

Answer 2

1.5 feet

Explanation:

Bob wants to plant a 7 foot by 10 foot garden.

Area =
`7*10=70` square feet

He wants to make a uniform border of petunias around the outside and still have 28 square feet to plant tomatoes and roses in the middle.

Means we have to factor 28 in a way that the length and width is less than 10 and 7.

28 = 2 x 2 x 7

Means 4 feet can be width and 7 feet the length of the area where tomatoes need to be planted.

So, we have
`10-7=3` feet less than outer garden means at each side
`3/2=1.5` feet decreases.

Similarly, we have
`7-4=3` feet less width and at each side it is 1.5 feet.

Therefore, the border of petunias will be 1.5 feet wide on all sides.