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A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?

Respuesta :

colella51
width = y
length = y+5
area = 104 = y x (y+5) = y^2 + 5y
y^2 + 5y -104 = 0
(y-8)(y+13)= 0
y= 8 because can't have negative lengths
length = 8 + 5 = 13

Answer:

13 feet

Step-by-step explanation:

Let x be the width of the rectangular garden.

We are given that the length of the garden is to be 5 feet longer than the width.

So, Length = x+5

Area of rectangle = [tex]Length \times Width[/tex]

                             = [tex]x \times (x+5)[/tex]

We are given that the area of the garden will be 104 square feet

So, [tex]x \times (x+5)=104[/tex]

[tex]x^2+5x -104=0[/tex]

[tex](x-8)(x+13)=0[/tex]

[tex]x=8,-13[/tex]

Since the width cannot be negative.

So, neglect -13

So, width = x = 8

Length = x+5 = 8+5 = 13

So, the length of the garden is 13 feet.

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