Question

The length of a rectangular garden is 17 feet longer than its width. If the area of the garden is 308 square feet, what are the dimensions of the garden?

A) First, write a quadratic equation in the from
aw^2+bw+c=0
you can solve to answer the question given. Let w be the width of the garden.

Use the variable w


B) Factor your equation from part [a] into the form


Answer: The factored equation is



C)Use your factored equation to find the length and width of the
feet.

Answer 1

A) w^2 +17w -308 = 0

B) (w -11)(w +28) = 0

C) length: 28 ft; width: 11 ft.

Explanation:

A)

If w is used to represent the width of the garden, then its length is w+17, and the relation to area is ...

w(w +17) = 308

w^2 +17w -308 = 0 . . . . the desired quadratic equation

__

B)

The equation can be factored as ...

(w -11)(w +28) = 0 . . . . . the factored equation

__

C)

The positive solution for w in the factored equation is w = 11. Then the length of the garden is ...

w +17 = 11 +17 = 28

The length and width of the garden are 28 feet and 11 feet, respectively.