Find the dimensions of a rectangle

by a visitor

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?
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

Comments for Find the dimensions of a rectangle

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Jun 03, 2015
niiice! NEW
by: Anonymous


Jun 01, 2015
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
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

May 21, 2015
by: Anonymous


Aug 04, 2014
Help pls
by: Joshua

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

Jul 24, 2014
wrong methods
by: ram

It is not helpful for all type calculation

Jul 02, 2014
by: Anonymous

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

Feb 19, 2014
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
by: Anonymous

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

Aug 19, 2010
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."


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