Question

14th question
plssss

Answer 1

let l be the length and b be the breadth of rectangle .

original area of rectangle = l × b
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step1 Find the area of rectangle if the length is increased by 5m and breadth is reduced by 4m:
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new length (l ) = ( l + 5 ) m

new breadth ( b) =( b - 4 ) m

new area = ( l + 5 ) × ( b - 4 )

according to first statement :
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original area - new area = 160 m^2

l × b - ( l + 5 )×( b - 4 ) = 160

lb - lb + 4l - 5b + 20 = 160

4l - 5b = 140 --------------------------------(1)
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step 2 Find the area of rectangle if the length is decreased by 10m and breadth is increased by 2m:
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new length ( l ) = ( l - 10 ) m

new breadth (b) = ( b + 2 ) m

new area = ( l - 10 )×( b + 2 )

according to second statement :
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original area - new area = 100 m^2

lb - ( l - 10 )×( b + 2 ) = 100 m^2

lb - lb - 2l + 10b + 20 = 100

10b - 2l = 80 => 2 ( 5b - l ) = 80

=> 5b - l = 40 -----------------------------(2)

by adding (1 ) and (2), we get

4l - 5b = 140

5b - l = 40
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4l - 5b + 5b - l = 140 + 40

3l = 180 => l = 60 m = length

put Value of 'l' in eq.(2) , we get

5b - l = 40

5b - 60 = 40

5b = 100 => b = 20 m

therefore , required dimensions are:
length of the rectangle ( l ) = 60 m
and breadth of the rectangle ( b) = 20m
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Your Answe: l = 60 m, b = 20 m
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