the perimeter of a rectangle is 70 cm if its breadth is 5 cm less than the length find its area
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Answered by
7
Answer:
300cm sq
Step-by-step explanation:
2(l+b)=70
b=l-5
2(l=l-5)=70
2(2l-5)=70
4l-10=70
4l=70+10=80
l=20
b=l-5=20-5=15
l*b=20*15=300 cm sq
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Answered by
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It is given that the breadth of the rectangle is 5 cm less than the length of the same rectangle.
Let the length of the rectangle be a cm, and breadth of the rectangle be ( a - 5 ) cm i.e. 5 cm less than a cm, which is the length of the rectangle.
Now,
Length of the rectangle is a cm
Breadth of the rectangle is ( a - 5 ) cm
According to the question :
Perimeter of the rectangle = 70 cm
=============
From the properties of rectangle, we know
Perimeter of rectangle = 2( length + breadth )
=============
Thus,
= > 2{ a cm + ( a - 5 ) cm } = 70 cm
= > 2( a cm + a cm - 5 cm ) = 2 x 35 cm
Cancelling 2 from both sides,
= > 2a cm - 5 cm = 35 cm
= > 2a cm = 40 cm
= > a cm = 20 cm
Hence,
Length of the rectangle = a cm = 20 cm
Breadth of the rectangle = ( a - 5 ) cm = ( 20 - 5 ) cm = 15 cm
=============
From the properties of rectangle, we know
Area of rectangle = length x breadth
=============
Therefore,
Area of this rectangle = 20 cm x 15 cm
Area of this rectangle = 300 cm²
Hence,
Area of the rectangle is 300 cm².
Let the length of the rectangle be a cm, and breadth of the rectangle be ( a - 5 ) cm i.e. 5 cm less than a cm, which is the length of the rectangle.
Now,
Length of the rectangle is a cm
Breadth of the rectangle is ( a - 5 ) cm
According to the question :
Perimeter of the rectangle = 70 cm
=============
From the properties of rectangle, we know
Perimeter of rectangle = 2( length + breadth )
=============
Thus,
= > 2{ a cm + ( a - 5 ) cm } = 70 cm
= > 2( a cm + a cm - 5 cm ) = 2 x 35 cm
Cancelling 2 from both sides,
= > 2a cm - 5 cm = 35 cm
= > 2a cm = 40 cm
= > a cm = 20 cm
Hence,
Length of the rectangle = a cm = 20 cm
Breadth of the rectangle = ( a - 5 ) cm = ( 20 - 5 ) cm = 15 cm
=============
From the properties of rectangle, we know
Area of rectangle = length x breadth
=============
Therefore,
Area of this rectangle = 20 cm x 15 cm
Area of this rectangle = 300 cm²
Hence,
Area of the rectangle is 300 cm².
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