Find the length and width of a rectangle

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

Answer
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

Average Rating starstarstarstar

Click here to add your own comments

Oct 15, 2016
Rating
star
no help NEW
by: Anonymous

no help at all >=(

Oct 15, 2016
Rating
star
no help NEW
by: Anonymous

no help at all >=(

Sep 08, 2016
Rating
starstarstarstarstar
8th grade problem NEW
by: Anonymous

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

Sep 07, 2016
Rating
starstarstarstarstar
HELP 7TH GRADE IS HARD NEW
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.

Aug 07, 2016
Rating
star
I didn't help NEW
by: Lola

Hi sorry it really didn't help me I have this sum:
The perimeter of a rectangle is 1200m.If it's length is twice the width,
A)Wat is the length of the field ?
B)give the width of the field?
C)calculate the area of the field?


I need the answer ASAP

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

Determine the value of L
Area=9u2

May 19, 2015
Rating
starstarstarstarstar
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
Rating
starstarstarstarstar
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?

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Measurements Library.

iPod Touch & iPhone
iPad
Graphs & Equations
Algebra
Exponents
Symmetry
Fractions
Measurements
Interest
Angles
Triangles
Useful Resources