451,091 views
32 votes
32 votes
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.

User Amarjit Singh
by
2.3k points

1 Answer

17 votes
17 votes

Answer:

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.

User Richert
by
2.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.