The perimeter of rectangular field is 28 cm and its area is 48 cm². Find its length and
breadth.
Answers
Given
Perimeter of Rectangular field is 28cm and it's area is 48cm².
To Find
We have to find its length and breadth
How to solve ?
step 1:Firstly we will apply perimeter or area formula of Rectangle and mark them Equation 1 and 2.
Step 2:From Equation 1 or 2 and we will convert the whole Equation either in the form of length or breadth and then substitute into another equation.
Step 3: We will find one value either l or b then again put into another Equation to find other value.
Since, perimeter of Rectangular field= 2(l+b)
Perimeter is 28cm
Our Equation becomes: 28= 2(l+b)----(1)
Area of Rectangular field= length * breadth
since ,area is 48cm²
Our Equation becomes: 48= l*b------(2)
From equation 1
=> 14 = l+b
l= 14-b----(3)
Substitute Equation 3 into 2
=> 48= (14-b)*b
=> 48= 14b-b²
=> 48-14b+b²
=> b²-14b+48
=> b²-8b-6b+48
=> b(b-8)-6(b-8)
=> (b-6)(b-8)
Makes equal to zero
we get b = 6 or b=8
Substitute b's value into equation 3
When b = 6
=>l= 14-6
length = 8
when b= 8
l= 14-8=6
Hence,length is 8cm or 6cm.
Breadth is 6cm or 8cm
Extra information=>
Area is Space or region which is covered by a solid object/figure it is said to be area of that object.
Area depends upon the dimensions of the figure.If dimensions is larger then larger will be the area of that object/figure and vice -versa.
Perimeter
Perimeter is the total distance occupy by a solid 2D figure around its edge.
Answer:
Answer :-
To find length and breadth of the rectangular field.
________________________________
Given,
perimeter = 28cm
and, area = 48cm²
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Perimeter of rectangle = 2(L+b)
=> 28cm = 2(L+b)
=> 14 cm = L +b
=> 14 - L = b...(I)
Now Area = L × b
=> 48cm² = L × b
here substitute the value of b and solve:-
=> 48cm² = L(14-L)
=> 48cm² = 14L - L²
=> L² -14L + 48 = 0
=> L² - 6L - 8L + 48 = 0
=> L( L - 6) - 8(L- 6) = 0
=> (L -8)(L-6) = 0
L = 8 or. L = 6
Now if L = 8
then b = 14 - L
=> 14 - 8
=> 6 cm
else L = 6
b = 14 - 6
=> 8 cm
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Hope it's helpful
Thank you