the lenght of a rectangle is 5 cm less than twice in its breadth if the length is decreased by 3 cm and breadth increased by 2 cm the perimeter of the resulting rectangle is 72 cm find the area of original rectangle
Answers
Step-by-step explanation:
Let the length be x
and the Breath be y
According to the question
x=2y-5 (equation 1)
Perimeter of rectangle=2(l+b)
72 cm = 2 (x-3 + y+2)
72=2(x+y-1)
72/2=x+y-1
36+1=x+y
x+y=37 (equation 2)
Putting the equation first into second equation, we get
2y-5 + y = 37
3y=37+5
3y=42
y=14
and x=2y-5
x=2×14-5
x=28-5
x=23
so,
length is 23 cm
and breath is 14 cm
Area of rectangle= l×b
= 23×14 cm^2
=322 cm^2
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Answer:-
The area of the original rectangle is 322 cm².
Explanation:-
Given:
Length of the rectangle is 2 cm less than twice it's breadth.
Perimeter of the resulting triangle= 72 cm
To find:
The area of the original triangle.
Solution:
Let the length be 'x'
and the breadth be 'y'
As it's given that, the length of rectangle is 5 cm less then twice it's breadth, The formed equation will be:
x + 2y = 5___________(i)
Again,
The length of new rectangle= (x-3)cm
The breadth of the rectangle= (y+2)cm
And, Perimeter of the resulting rectangle is 72cm respectively.
Now, we know that the formula of the perimeter of a rectangle is:-
Perimeter= 2(length+breadth) unit
=> 2(x-3+y+2) = 72
=> x-3+y+2 = 72/2
=> x+y-1 = 36
=> x+y = 36+1
=> x+y = 37__________(ii)
Putting, the value of 'x' from the first equation into the second equation.
=> x + y = 37
=> (2y - 5) + y = 37
=> 2y - 5 + y = 37
=> 3y - 5 = 37
=> 3y = 37 + 5
=> 3y = 42
=> y = 42/3
=> y = 14
Putting, the value of 'y' in the first equation.
=> x = 2y - 5
=> x = 2 × 14 - 5
=> x = 28 - 5
=> x = 23
Therefore, the length of the original rectangle is 23 cm and the breadth of the original rectangle is 14 cm.
Now,
We know that the formula of finding the area of the rectangle is:-
Area= (Length×Breadth)unit²
=> Area= (14×23) cm²
=> Area= 322 cm²