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:

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

2) Solve the Quadratic Equation
Notice that, now we have a quadratic equation:

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

Now, since w is the width of a rectangle. There is no way it can be a negative number. Therefore, w must be 5.

With w = 5. The...

...and the...

Below is the rectangle with its dimensions:

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

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Oct 30, 2023
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Mar 07, 2023
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Nov 15, 2020
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Thanks NEW
by: Anonymous

Thanks for your answer and solution but what sign I will put? is it
A. W IS LESS THAN OR EQUAL TO 5; OR L IS LESS THAN OR EQUAL TO 9

B. W IS GREATER THAN OR EQUAL TO 5; L IS GREATER THAN OR EQUAL TO 9

C. W>5;L>9

D. W<5;L<9

I need the answer asap but its okay if you don't know/youll not reply:))

thanks again

Nov 13, 2020
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Jan 23, 2018
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Nov 06, 2017
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I have figured this out probably by chance.
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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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I mostly want to know where the twelve came from.

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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.

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Feb 25, 2016
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kindly answer this math problem:
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Nov 27, 2015
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Nov 04, 2015
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My problem is: if there are 45 total tiles what are the dimensions?

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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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