Mona has 160 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed are
1 answer:
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9 :
Given,
Perimeter = 88 units
Base = x + 4
Height = x - 6
= > Perimeter of Rectangle = 2( base + height )
= > 88 = 2{ ( x + 4 ) + ( x - 6 ) }
= > 88 / 2 = { x + 4 + x - 6 }
= > 44 = 2x - 2
= > 46 = 2x
= > 46 / 2 = x
= > 23 = x
Therefore,
Length of base = ( x + 4 ) units = ( 23 + 4 ) units = 27 units
Length of height = ( x - 6 ) units = ( 23 - 6 ) units = 17 units
10 :
Given,
First integer = x
Second integer = x + 2
Third Integer = x + 4
Given that the sum of all integers is 36
= > ( x ) + ( x + 2 ) + ( x + 4 ) = 36
= > x + x + 2 + x + 4 = 36
= > 3x + 6 = 36
= > 3x = 30
= > ( 3x ) ÷ ( 3 ) = ( 30 ) ÷ ( 3 )
= > x = 10
Value of first integer = x = 10
Given,
Perimeter = 88 units
Base = x + 4
Height = x - 6
= > Perimeter of Rectangle = 2( base + height )
= > 88 = 2{ ( x + 4 ) + ( x - 6 ) }
= > 88 / 2 = { x + 4 + x - 6 }
= > 44 = 2x - 2
= > 46 = 2x
= > 46 / 2 = x
= > 23 = x
Therefore,
Length of base = ( x + 4 ) units = ( 23 + 4 ) units = 27 units
Length of height = ( x - 6 ) units = ( 23 - 6 ) units = 17 units
10 :
Given,
First integer = x
Second integer = x + 2
Third Integer = x + 4
Given that the sum of all integers is 36
= > ( x ) + ( x + 2 ) + ( x + 4 ) = 36
= > x + x + 2 + x + 4 = 36
= > 3x + 6 = 36
= > 3x = 30
= > ( 3x ) ÷ ( 3 ) = ( 30 ) ÷ ( 3 )
= > x = 10
Value of first integer = x = 10
