Find the dimensions of a rectangle

by a visitor

Question
The area of a rectangle is 45 square cm. If the length is 4 cm greater than the width, what is the dimensions of the rectangle?

Answer
The picture below shows the rectangle with the area of 45cm2. Now, let the width be w. Since, the length is 4cm greater than the width, the length will be w+4 cm. 

rectangle with the length w+4 and the width w

Before we can find the dimensions of the rectangle, we need find w first. Here's how:

1) Write an equation that relates 45cm2, w+4 and w.
To do so, we know that the area of the rectangle, 45cm2 can be found by multiplying w with  w+4. Hence, we have: 

the equation, w(w+w) = 45

To continue, we need to remove the bracket and simplify the equation. This is shown below:  

removing the brackets in w(w+4)


2) Solve the Quadratic Equation
Notice that, now we have a quadratic equation:
 
the quadratic equation, w^2 +4w -45 = 0

To find w, we need to solve the quadratic equation. One way to do so is to factorize the quadratic equation. Hence, we have:

w is -9 or 5

Now, since w is the width of a rectangle. There is no way it can be a negative number. Therefore, w must be 5. 
w is 5
With w = 5. The...
the length of the rectangle is 9cm

...and the... 
the width of the rectangle is 5cm
Below is the rectangle with its dimensions:
 

rectangle with the length of 9cm and the width of 5cm


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Oct 20, 2020
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How to answer this problem
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Hi guys ban you help me with this.

Mr. Radace will be asking to the carpenter to construct a square floor with the area of 64 square meter. In his approximation based from the house plan, the floor must in the area of 100 square meter.

1. Draw a diagram to illustrate the house floor area.

2. What is the possible dimension of the new area of the house floor?

3. How did you determine the possible dimensions of the floor?

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5. What is the difference of new area to the old area if the side will increase to 4 meter from the 64 square meter area?

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i dont get it.
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Aug 12, 2020
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Thank you!
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Very useful, was in class working on this and this helped a lot. Would definitely keep using this. Nothing out there like this. Thank you to the creators!

Jun 16, 2018
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This page was very helpful in helping me learn how do do this math problem. Thanks for the help.

Jun 10, 2018
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How would you describe the equation formulated?

Apr 17, 2018
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Mar 22, 2018
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Jan 23, 2018
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uh
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aye yo i didnt understsnd this lololololololololol

Nov 06, 2017
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people who live in china have only one child
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idk why pls help

Nov 01, 2017
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Help
by: Anonymous

I have figured this out probably by chance.
I have to show work and am having a hard time putting it together.
I have a rectangle with area of 209ft2
divided into a square and a rectangle. The rectangle part is 8 ft wide.
I found that the square is 11x11 and rectangle would be 11x8

I have no idea please help.

shagnola@hotmail.com


Aug 22, 2017
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Aug 20, 2017
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Thank you very much! •u• I found this very helpful and even had fun solving my math homework, which is a very rare thing to happen!

Jul 02, 2017
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Helpful~!!
by: StuDYING

Thank you very much! •u• I found this very helpful and even had fun solving my math homework, which is a very rare thing to happen!

May 25, 2017
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ughh
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What is the problem dosent give you an area...this is the problem: The floor of a rectangular cage has a length 4 feet greater than its width, w. James
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The answer turned out to be: N = w2 + 8w + 12

I mostly want to know where the twelve came from.

Email me @ nadiaelizabeth2002@gmail.com if you're willing to help me.

May 14, 2017
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Thank you so much for making this! Really helped me with my Algebra 1 homework!

Apr 26, 2017
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The dimensions would be 50 by 10, 50 being the length or width and 10 being length or width or vice versa. 50 * 10 = 500 and 50 + 50 + 10 + 10 = 120.

Feb 09, 2017
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Not for use
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It need to be updating still lots for question ar there on this basis

Feb 29, 2016
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Nov 27, 2015
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My problem is: if there are 45 total tiles what are the dimensions?

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Jun 01, 2015
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Reply to comment from May 31, 2015
by: Visual Math

The perimeter of a rectangle is its two times its length and width combined, expressed in this way:

P = 2 x (l + w)

Now then, given that the length is three cm more than twice the width, we can express the length in terms of the width in this way:

l = 2w + 3

Thus, if we replace all the variables with the information we have, we can find out its dimensions:

P = 2 x (l + w)
84 = 2 x ((2w + 3) + w)
84 = 2 x (3w + 3)
84 = 6w + 6
6w = 84 - 6
6w = 78
w = 78/6
w = 13cm

Given that w is 13cm, we can then use it to find l:

l = 2w + 3
l = 2(13) + 3
l = 26 + 3
l = 29cm

May 31, 2015
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Help please
by: Anonymous

The length of a rectangle is three cm more than twice the width. If the perimeter is 84 cm what are the dimensions

Aug 04, 2014
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Help pls
by: Joshua

What if we dont have the 45, what if the equation is k(k+5)=d

Jul 24, 2014
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wrong methods
by: ram

It is not helpful for all type calculation

Jul 02, 2014
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Meh
by: Anonymous

Alright, but what about (x-3)(x+2)=18cm(squared) and (x+3)(x-2)=18cm(squared)

Feb 19, 2014
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help please to solve
by: Anonymous

area equals 84
the length is 5 more than the width find the dimensions of the rectangle

May 13, 2011
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awesome
by: Anonymous

it helped me in passing to the higher level in high school.

Aug 19, 2010
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:D
by: syntax_error

it helped me do my homework but I encountered some uncertainty towards the end of the process...

kindly...this is the problem..

"the length of the rectangular lot is 2 meters more than its width. Find its dimension if the area is 195 meters square each dimension it made is 1m longer."

thanks!

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