MATH SOLVE

4 months ago

Q:
# Rosa has a rectangle shaped backyard where the length is two less than twice the width. If the area of the garden is 420 square feet, find the dimensions of Rosa's garden?

Accepted Solution

A:

The expression for the area of a rectangle is given by:

A = (w) * (l)

Where,

l: long

w: width

the length is two less than twice the width:

l = 2w-2

Substituting the values:

420 = (w) * (2w-2)

We rewrite the expression:

210 = (w) * (w-1)

210 = w ^ 2-w

w ^ 2-w-210 = 0

The roots of the polynomial are:

w1 = -14

w2 = 15

We discard the negative root.

Width:

w = 15

Long:

l = 2w-2

l = 2 (15) -2

l = 30-2

l = 28

Answer:

the dimensions of Rosa's garden are:

w = 15 feet

l = 28 feet

A = (w) * (l)

Where,

l: long

w: width

the length is two less than twice the width:

l = 2w-2

Substituting the values:

420 = (w) * (2w-2)

We rewrite the expression:

210 = (w) * (w-1)

210 = w ^ 2-w

w ^ 2-w-210 = 0

The roots of the polynomial are:

w1 = -14

w2 = 15

We discard the negative root.

Width:

w = 15

Long:

l = 2w-2

l = 2 (15) -2

l = 30-2

l = 28

Answer:

the dimensions of Rosa's garden are:

w = 15 feet

l = 28 feet