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


Comments for Find the dimensions of a rectangle

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Jul 24, 2014
wrong methods NEW
by: ram

It is not helpful for all type calculation

Jul 02, 2014
Meh NEW
by: Anonymous

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

Jun 24, 2014
BOO U SUCK NEW
by: Anonymous

BOO YOU SUCK

Feb 19, 2014
help please to solve NEW
by: Anonymous

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

Feb 10, 2014
Boo NEW
by: Anonymous

Boo it didn't help

Feb 12, 2013
yjh
by: Anonymous

hi

May 13, 2011
awesome
by: Anonymous

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

Aug 19, 2010
: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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