Question 63843: Find the dimensions of a rectangle whose perimeter is 46 meters and whose area is 126 meters
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! QUESTION
Find the dimensions of a rectangle whose perimeter is 46 meters and whose area is 126 meters
ANSWER:(Some times you may find some steps repeating, because if some default.Please make it out. Still you have doubt, I will help you.)
Perimeter of a rectangle = 2 ( length + breadth )
46 = 2 ( length + breadth )
That is, Length + breadth = 46/2
Length + breadth = 23
length = 23 - breadth
==> L = 23 - B ---------------------(1)
Area is given as 126 meters
Tat is,
L * B = 126 ------------------------(2)
Now substitute the value, L= 23 - B in the second equation,
===> ( 23 - B ) * B = 126
Remove the brackets, by multiplying term by term,
===>23 * B - B * B = 126
==> 23B - B^2 = 126
By arranging the terms, we have a quadratic equation here,
====> -B^2 + 23B = 126
Subteract 126 from both sides of the equation,
===> -B^2 + 23B -126 = 126 -126
===> -B^2 + 23B -126 = 0
This is a quadratic equation ( in variable B )
Using quadratic formula, find solutions ( All possible values of B) of the
equation.
Compare the given equation with the standard equation, ax^2 + bx + c = 0.
Then we have,
a = -1 b = 23 and c = -126
We have the quadratic formula,
Here we use the same formula, but for the variable B,
Substitute the values, a, b and c
===> 
===> 
===> 
===> B = (-23 + 5 )/-2 or B = (-23 - 5 )/-2
===> B = (-18 )/-2 or B = (-28 )/-2
===> B = 9 or B = 14
Now, Find out correspopnding values of L
When B = 9,
we have L = 23 - 9 = 14
When B = 14, L = 23 - 14 = 9
So we have two pairs of values,
(Here breadth means width)
Length = 14, breadth = 9
Length = 9 and breadth = 14
Hope You understood.
Regards.
praseenakos@yahoo.co.in
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