Lesson Relationship between area and perimeter of a rectangle

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About Timnewman: Tim is from the department of mathematics Kogi State college of education Ankpa. Kogi State,Nigeria. Feel free to email me at timtimazubuike@gmail.com for the solution of your mathematics problem or explanation of any concept in maths.it is absolutel

Relationship between area and perimeter of a rectangle

This lesson is a continuation of the lesson
BASIC FORMULAE FOR FINDING AREA OF A RECTANGLE 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;,

A=LW
P=2(L+w)

where L=length,W=width,P=perimeter and A=area,

see the example below

EXAMPLE 1

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.

SOLUTION

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.

Example 2

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

Solution

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.

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