the perimeter of rectangular field is28cm and it's area is 48cm². find it's length and breadth
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the perimeter of rectangular field is28cm and it's area is 48cm². find it's length and breadth
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Answer:
Length = 8cm Breadth =6cm
Step-by-step explanation:
As we know that the perimeter of rectangular field = 28 cm
And
Area = 48 cm²
so
2(l+b) = 28 cm
l+b = 28÷2= 14 cm
and area of rectangle is l×b =48 cm²
so now
l+b = 14 cm
l×b =48 cm
so by this way we have to find the thing which gave us 14 cm on adding and 48 on multiplying .
8+6 = 14 cm
8×6 = 48cm²
(hope it's help you )
Verified answer
Given:-
To Find:-
Formula used:-
Solution:-
Firstly,
Perimeter of rectangle = 2(L + B)
[tex]⟹28 = 2(L + B)[/tex]
[tex]⟹L + B=14[/tex]
[tex]⟹L =14-B[/tex] ____ {1}
Now,
Area of rectangle = L × B
[tex]⟹48 = L × B[/tex]
Putting the value of L in it,
[tex]⟹48 = (14-B) × B[/tex]
[tex]⟹48 = 14B-B²[/tex]
[tex]⟹B²-14B+48=0[/tex]
By Middle term split,
[tex]⟹B²-(8+6)B+48=0[/tex]
[tex]⟹B²-8B-6B+48=0[/tex]
[tex]⟹B(B-8)-6(B-8)=0[/tex]
[tex]⟹(B-8)(B-6)=0[/tex]
[tex]⟹B-8=0 \: or\: B-6=0[/tex]
[tex]⟹B=8 \: or\: B=6[/tex]
Putting values in {1},
If B = 8cm
[tex]⟹L =14-8[/tex]
[tex]⟹L =6cm[/tex]
If B = 6cm
[tex]⟹L =14-6[/tex]
[tex]⟹L =8cm[/tex]
Hence, The Length and Breadth of the rectangular field is either 8cm and 6cm respectively or 6cm and 8cm respectively.
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