Respuesta :
Answer:
1.5 feet
Step-by-step explanation:
Bob wants to plant a 7 foot by 10 foot garden.
Area = [tex]7\times10=70[/tex] 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 [tex]10-7=3[/tex] feet less than outer garden means at each side [tex]3/2=1.5[/tex] feet decreases.
Similarly, we have [tex]7-4=3[/tex] 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.
Answer:
Width of the border is 1.5 feet.
Step-by-step 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,
[tex](7 - 2x)(10 - 2x)=28[/tex]
[tex]70 -14x-20x + 4x^2=28[/tex]
[tex]4x^2 -34x+70-28=0[/tex]
[tex]4x^2 -34x+42=0[/tex] ( Combine like terms )
[tex]4x^2-(28+6)x+42=0[/tex] ( Middle term splitting )
[tex]4x^2-28x-6x+42=0[/tex]
[tex]4x(x-7)-6(x-7)=0[/tex]
[tex](4x-6)(x-7)=0[/tex]
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.
