110k views
4 votes
The length of a rectangle is 7ft more than double the width, and the area of the rectangle is 99ft^(2). Find the dimensions of the rectangle.

User Robev
by
7.9k points

1 Answer

4 votes

Answer:

Width = 5.5 ft.

Length = 18 ft.

Explanation:

Relating the length to the width:

Since the length (L) is 7 ft. more than double the width (W), we can represent this with the following equation:

L = 2W + 7

Formula for the area of a rectangle:

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

A = LW, where

  • A is the area in units squared,
  • L is the length,
  • and W is the width.

Finding the width:

Thus, we can find the width (W) by substituting 99 for A and 2W + 7 for L in the area formula:

99 = (2W + 7)(W)

99 = 2W^2 + 7W

Converting the quadratic to standard form:

  • We can solve for W using the quadratic formula.

Before we can use the quadratic formula, we need to convert 99 = 2W^2 + 7W to the standard form of a quadratic, whose general equation is given by:

ax^2 + bx + c = 0, where

  • a, b, and c are constants.

Thus, we can convert to standard form by moving 2W^2 and 7W to the left-hand side:

(99 = 2W^2 + 7W) - 2W^2 - 7W

-2W^2 - 7W + 99 = 0

Thus, -2 is our a value, -7 is our b value, and 99 is our c value.

The quadratic formula:

The quadratic formula is given by:

x = (-b ± √b^2 - 4ac) / 2a, where

  • x are the solutions (the ± indicates that it is possible to have two solutions to a quadratic since squaring a positive and negative number gives us a positive number).

Thus, we can find the width (W) by plug in -2 for a, -7 for b, and 99 for c in the quadratic formula:

W = (-(-7) ± √(-7)^2 - 4(-2)(99)) / 2(-2)

W = (7 ± √841) / -4)

W = (7 ± 29) / -4

Now we can start separating the positive and negative solution:

W = -7/4 + (-29/4) and W = -7/4 - (-29/4)

W = -7/4 - 29/4 and W = -7/4 + 29/4

W = -9 and W = 5.5

Since we can't have a negative dimension, the width is 5.5.

Finding the length (L):

We can now find the length (L) of the rectangle by substituting 99 for A and 5.5 for W in the rectangle area formula:

(99 = 5.5L) / 5.5.

18 = L

Thus, the length (L) of the rectangle is 18 ft.

We know that our answers are correct since double the width is 11 as 5.5 * 2 = 11 and 7 more than this is 18 since 11 + 7 = 18.

User Duloren
by
7.8k points

Related questions

1 answer
2 votes
81.1k views
asked Apr 27, 2017 143k views
Khamitimur asked Apr 27, 2017
by Khamitimur
7.6k points
1 answer
0 votes
143k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.