Question

The length of a rectangle is 9 inches longer than the width. If the area is 205 square inches, find the

rectangle's dimensions. Round your answers to the nearest tenth of an inch.

Answer 1

L=19.5in w=10.5in

Explanation:

Draw a rectangle. If the length is 9 inches longer than its width, we can write the width as "w" and the length as the width + 9

Area is (width)(Length) = (width)(width+9)

W

----------

| |

| |

| | L = w+9

| |

| |

-----------

A = (w+3)(w)

A = w2 + 9w = 205.

(Problem states that area is 205 sq in)

Need to solve this quadratic equation

w2 + 9y - 205 = 0

Factor:

(w - 10.51) (w + 19.51) = 0

So

w - 10.51 = 0. or. w + 19.51 = 0

Solve these and get

w = 10.51. or. w = -19.51

Only one that makes sense in real life is the positive one.

So the dimensions are

Width = 10.51 inches

Length = 19.51 inches