Find the length and width of a rectangle

Draw a rectangle that has a perimeter of 18 cm and an area greater than 18 What are the dimensions?

STEP 1:    It will be helpful if you can recall the basic properties of a rectangle. A rectangle is defined by the dimensions length and width. It has four sides, and also the opposite sides of a rectangle have the same length.

You are given the perimeter of a rectangle. The perimeter, as you know, is the total distance along the outside of the rectangle. The formula used to calculate perimeter is:
perimeter of a rectangle formula
In the formula, the variables l and w denote the length and width of the rectangle, respectively.

STEP 2:    Since you know the value of the perimeter, you can make the replacement in the formula.
substituting the perimeter with 18
By dividing both the sides by 2, the equation changes to
9 = l + w, or l + w = 9.

STEP 3:    Think of the possible dimensions the rectangle can have if the sum of the length and width equals 9 cm. But, it is given that area of the rectangle has to be greater than 18 sq. cm. This means that the product of the length and width must be greater than 18.

Try different values for l and w such that the sum equals 9. Find the corresponding products, and then make a table of values.
length-width combination table
If you observe the table, then you can find that the area of the rectangle is greater than 18 only when the dimension of the rectangle is either 4 cm by 5 cm, or 5 cm by 4 cm.

STEP 4:    Choose any of the two desirable dimensions. Then, finally draw the rectangle.
rectangle with length 5cm and width 4cm

Comments for Find the length and width of a rectangle

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Mar 03, 2018
Not Clear
by: Anonymous

Please make it more understandable. I didn't understand the table thing at all...

Nov 14, 2017
Don’t insult my intelligence.
by: Anonymous

I have a problem that gives me the area, and only the area. I need to know how to find both length and width when neither are present and the only thing given to me is just the area.

I already know these basics and I came here for help with more complicated problem that required something more than this basic formula.

Nov 06, 2017
well then
by: charley

not really helpful.. Sorry.

Sep 13, 2017
Mathematics master
by: Anonymous

No help ☹️

Dec 22, 2016
by: ashaboluwatife

please help me find the length of rectangle whose perimeter and area add me on

Sep 08, 2016
8th grade problem
by: Anonymous

8th grade math problem- a rectangle has an area of 90 units. what is the rectangles length and width?

Sep 07, 2016
by: Anonymous

Hi is there an easier way to solve this. I only have the area and need to find possible lengths and width. Thanks.

Apr 08, 2016
Finding side length (Given Area)
by: Anonymous

Determine the value of L

May 19, 2015
Area calculations
by: Visual Math

The formula for the area of a rectangle is A = w x l; if the area is given and the width is a fraction of the length, the formula can be expressed thus:

A = (a/b x l) x l

Since we are looking for the length, we invert the formula for the area of a rectangle:

l = A/w

Based on the information that the width is a fraction of the length, the formula would thus be in this form:

l = A/(a/b x l)

Now, let's rearrange the formula:

l(a/b x l) = A
l x a/b x l = A
l^2 = A/(a/b)
l^2 = Ab/a
l = √(Ab/a)

So, for example, if it is given that the area is given as 6cm^2, and the width is 2/3 of the length, then, using the formula above, we would get the following:

l = 6/(2/3 x l)
l(2/3 x l) = 6
l^2 = 6/(2/3)
l^2 = 9
l = 3cm

Feb 08, 2014
Area calculation
by: Anonymous

How do you find the length of rectangle if the area is given and the width is a fraction of the length?

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