the perimeter of a rectangular peice of land I 130m and its area is 1000m^2. Determine its dimensions.
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Let length be 'l' and breadth be 'y'
Perimeter = 2( l + b ) = 130
l = 65 - b ...
Area = l × b = 1000m²
we know l = 65 - b
so,
( 65 - b ) × b = 1000
65b - b² = 1000
b² - 65b + 1000 = 0
b² - 25b - 40b + 1000 = 0
b( b - 25 ) - 40 ( b - 25 ) = 0
( b - 40 ) ( b - 25 ) = 0
b = 40 or 25.......
when b = 40m
l = 65 - 40
= 25m......
when b = 25m
l = 65 - 25
= 40m......
We know that 'l' should be larger than 'b'
so dimensions are 40m × 25m
Hope it helps
Let length be 'l' and breadth be 'y'
Perimeter = 2( l + b ) = 130
l = 65 - b ...
Area = l × b = 1000m²
we know l = 65 - b
so,
( 65 - b ) × b = 1000
65b - b² = 1000
b² - 65b + 1000 = 0
b² - 25b - 40b + 1000 = 0
b( b - 25 ) - 40 ( b - 25 ) = 0
( b - 40 ) ( b - 25 ) = 0
b = 40 or 25.......
when b = 40m
l = 65 - 40
= 25m......
when b = 25m
l = 65 - 25
= 40m......
We know that 'l' should be larger than 'b'
so dimensions are 40m × 25m
Hope it helps
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