How do you find the length and width if you have the area and perimeter?

← Previous 1 2 3 4 Next →

The rectangle below has a perimeter of 54. Find the lengths of the unknown side. That is, find S.

Possible Answers:

Explanation:

For a rectangle, its perimeter is the sum of all for sides. We can write

Simplify

Solve for S

Given a rectangle with a length

 units longer than its width and an area of  square units, find the length of the rectangle's shortest side.

Possible Answers:

Correct answer:

Explanation:

The given rectangle has a length that is 

 units longer than its width. This can be expressed in the following equation, where  is the length and  is the width of the rectangle.

Since the area of the rectangle is equal to its length multiplied by its width (

), and the area of the rectangle is given, the following equation must be true.

Replacing 

 in this equation with its value stated in the first equation results in the following.

Distribute the variable into the parentheses.

Factor the polynomial.

 and  are both solutions for this equation, but  is not valid as a width for a rectangle. The width of the rectangle is  units, which is the shorter side since the length is  units longer .

There is a regtangular fence surrounding a park. The perimeter of the fence is 

. What is the width of the fence if the length is ?

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

The formula for the perimeter of a rectangle is:

, where represents the length and represents the width.

We know the perimeter of the rectange is 

and the length is . Plugging these values into the equation, we get:

 

  

A rectangle has a perimiter of 36 inches and a length of 12 inches.  What is the width of the rectangle in inches?

Possible Answers:

Correct answer:

Explanation:

To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides.  This number divided by 2 is the width. 

A rectangle four and a half times as long as it is wide has perimeter of 272 centimeters. To the nearest tenth of a centimeter, how wide is it?

Possible Answers:

Correct answer:

Explanation:

If we call the width of this rectangle

, then its length  can be restated as, or, equivalently, .

The perimeter can then be written as:

Since the perimeter of the rectangle is 272 cm, we can set up the following equation:

The width, in cm, of a rectangular fence is 2 more than half its length, in cm. Which of the following gives the width, w cm, in terms of length, l cm, of the rectangular fence?

Possible Answers:

Correct answer:

w = ½ l + 2

Explanation:

To find the width, we must take half of the length, which means we must divide the length by 2. Then we must take 2 more than that number, which means we must add 2 to the number. Combining these, we get:

w = ½ l + 2

The width of a rectangle is 2 inches longer than 3 times its length.  Which of the following equations gives the width, w, of the rectangle in terms of its length, l,?

Possible Answers:

Correct answer:

w = 3l + 2

Explanation:

The width equals 3 times the length, so 3l, plus an additional two inches, so + 2, = 3l + 2

Your dad shows you a rectangular scale drawing of your house. The drawing is 6 inches by 8 inches. You're trying to figure out the actual length of the shorter side of the house. If you know the actual length of the longer side is 64 feet, what is the actual length of the shorter side of the house (in feet)?

Possible Answers:

Explanation:

We can solve this by setting up a proportion and solving for x,the length of the shorter side of the house. If the drawing is scale and is 6 : 8, then the actual house is x : 64. Then we can cross multiply so that 384 = 8x. We then divide by 8 to get x = 48. 

If the perimeter of a rectangle is 

 and the length of the rectangle is , what is the width of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle.

We can then manipulate this equation to find the width.

Now, plug in the information given by the question to find the width.

If the perimeter of a rectangle is 

 and the length of the rectangle is , what is the width of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle.

We can then manipulate this equation to find the width.

Now, plug in the information given by the question to find the width.

← Previous 1 2 3 4 Next →

John
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Sociology.

Lucero Juliana
Certified Tutor

Kendall College, Bachelor in Arts, Business Administration and Management.

Aaron
Certified Tutor

Tulsa Community College, Associate in Science, Mechanical Engineering.

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105

Or fill out the form below: