Lesson Relationship between area and perimeter of a rectangle

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<H2>Relationship between area and perimeter of a rectangle</H2>

This lesson is a continuation of the lesson 
&nbsp; <A HREF=http:/www.algebra.com/algebra/homework/-BASIC FORMULAE FOR FINDING AREA OF A RECTANGLE.lesson>BASIC FORMULAE FOR FINDING AREA OF A RECTANGLE</A>&nbsp; and it will help you to solve harder problems that relates to area and perimeter of a rectangle.

We shall consider two example here to enable you perform better when such problem is given to you.

In the previous lesson, we found that area and perimeter of a triangle is given by;,

<H2>A=LW
       P=2(L+w)</H2>
 
where L=length,W=width,P=perimeter and A=area,

<H2>see the example below </H2>

<H3>EXAMPLE 1</H3>
 The length of a rectangle is two more Than the width,if the area of the rectangle is 15cm^2,find the perimeter of the rectangle.

<H2> SOLUTION</H2>
Let width be w,
length =w+2
since Lw=15cm
Therefore,
(w+2)w=15

w^2+2w=15
 w^2+2w-15=0

factorize the quadratic equation,we have;

(w+5)(w-3)=0 
This means that

w+5=0        or  w-3=0
  then
w=-5cm or w=3cm

But w=-5 is not the solution since width cannot be negative.

Therefore,width is 3cm.
 
Recall that length=w+2
        but w=3cm
Hence,
L=3+2
L=5cm.

The length and width of the rectangle is 5cm and 3cm respectively.

Hence,
perimeter (P)=2(L+W)
but L=5cm,w=3cm
 Perimeter (P)=2(5cm+3cm)
      =2(8cm)
=16cm.

The perimeter of the rectangle is  16cm.

<H2>Example 2</H2>

The perimeter of a rectangle is 16cm if the its length is 5cm,find the area of the rectangle.

<H2>Solution</H2>   
   Before wee find the area of the rectangle,,we must first find the width of the rectangle.

From our question,

perimeter P=2(l+w)=16

length =5cm,
Then,
2(5+w)=16
10+2w=16
2w=16-10
2w=6
w=3

Now,length=5cm,w=3cm

Therefore Area A=Lw
A=5(3)
A=15cm^2

In  conclusion  ,  it  is  advisable  to  make  sure  that  when  dealing  with  area  and   perimeter  of  a  rectangle  ,  you  must  obtain  the  parameters  that  will  help  you  to  find  the  area  or  the  perimeter  you  are  looking  for.

Note:These  parameters  involves  length  and width  of  the rectangle.