The volume of Olivia's rectangular lunchbox is 240 cubic inches. The lunchbox is 3 inches deep, and its length is 2 inches more than its width. How wide is Olivia's lunchbox? (This is break homework)
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2
Heya
Volume of lunchbox is 240cubic inches
Let the width be x
Length be (x+2)
Volume of cuboid = lbh
240 = x(x+2)(3)
240/3 = x²+2x
80 = x²+2x
x²+2x-80 = 0
x²+10x-8x-80=0
x(x+10)-8(x+10)=0
(x+10)(x-8)=0
x+10=0 => x=-10
x-8=0 => x=8
As length can't be negative it is 8
Width is 8inches
Length is 8+2=10inches
Hope it helps
Volume of lunchbox is 240cubic inches
Let the width be x
Length be (x+2)
Volume of cuboid = lbh
240 = x(x+2)(3)
240/3 = x²+2x
80 = x²+2x
x²+2x-80 = 0
x²+10x-8x-80=0
x(x+10)-8(x+10)=0
(x+10)(x-8)=0
x+10=0 => x=-10
x-8=0 => x=8
As length can't be negative it is 8
Width is 8inches
Length is 8+2=10inches
Hope it helps
Answered by
6
Volume = 240 in³
Depth = 3 in
Define x:
Let x be the width
The length = x + 2
Find x:
Volume = Length x Breadth x Height
240 = ( x + 2) (x ) (3)
80 = x² + 2x
x² + 2x - 80 = 0
(x - 8) (x + 10) = 0
x = 8 or x = -10 (rejected, x cannot be negative)
Find the width:
Width = x = 8 inches
Answer: The width is 8 inches
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