Question

Next A rectangular garden is 15ft longer than it is wide. Its area is 2200ft². What are its dimensions?

Answer 1

The dimensions of the rectangular garden are 55 feet in length and 40 feet in width.

Step-by-step explanation:

To determine the dimensions of the rectangular garden, let's denote the width as w and the length as
`l`. According to the given information, the length is 15 feet longer than the width, so we can express the length in terms of the width as
`l` = w + 15. The area (A) of a rectangle is given by the formula A =
`l` × w.

Given that the area is 2200 square feet, we can set up the equation:

(w + 15)× w = 2200

Expanding and rearranging the equation:

`w^2`+ 15w - 2200 = 0

Now, we can solve for w using the quadratic formula:

`\[ w = \frac{{-b + \sqrt{{b^2 - 4ac}}}}{2a} \]`

For our equation, a = 1, b = 15, and c = -2200. Plugging in these values:

`\[ w = \frac{{-15 + \sqrt{{15^2 - 4(1)(-2200)}}}}{2(1)} \]`

Solving further gives two possible solutions for w , but since the width cannot be negative, we discard the negative solution. Therefore, w = 40 . Now, we can find the length (
`l` ):

`l` = w + 15 = 40 + 15 = 55

Hence, the dimensions of the rectangular garden are 55 feet in length and 40 feet in width.

Answer 2

The dimensions of the rectangular garden, which is 15ft longer than it is wide and has an area of 2200ft², are 40 feet by 55 feet.

Step-by-step explanation:

To find the dimensions of a rectangular garden that is 15ft longer than it is wide with an area of 2200ft², let's designate the width of the garden as w feet. Thus, the length will be w + 15 feet. Since area is length times width, we can set up the following equation:

w(w + 15) = 2200

Solving this quadratic equation to find the value of w, we get:

w² + 15w - 2200 = 0

To solve the quadratic, we look for factors of -2200 that add up to 15. We find that 55 and -40 satisfy this condition. Therefore, the quadratic factors as:

(w + 55)(w - 40) = 0

To find the width, we set each factor equal to zero and solve for w:

w + 55 = 0 → w = -55 (not a valid solution for width)

w - 40 = 0 → w = 40

Thus, the width of the garden is 40 feet, and its length is w + 15 = 40 + 15 = 55 feet.

The dimensions of the garden are 40 feet by 55 feet.