Question

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?

Answer 1

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 = $Length \times Width$

                             = $x \times (x+5)$

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

So, $x \times (x+5)=104$

$x^2+5x -104=0$

$(x-8)(x+13)=0$

$x=8,-13$

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.

Answer 2

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