Respuesta :
The dimensions of the square based prism that holds coloured pencils has a length dimension that is 13 centimetres greater than its width is 2cm x 2cm x 15cm
Let the length of the pencil be represented by l
Let the width be represented by w
The length is 13 centimeters greater than the width
This can be represented mathematically as:
l = w + 13........(1)
The area = Length x Width
Area = lw............(2)
Substitute equation (1) into equation (2)
Area = w(w + 13)...........(3)
The volume of the box = 60 cubic centimetres.
Volume = Area x width
60 = w(w + 13) x w
60 = (13 + w)w²
w³ + 13w² - 60 = 0
Solving the cubic equation above:
w = 2, -12.62, or -2.38
Since the width cannot be negative
w = 2 cm
The length of the pencil = w + 13
The length of the pencil = 2 + 13
The length of the pencil = 15 cm
The length of the pencil = The height of the prism = 15 cm
Since the prism is square-based:
the length = the width
Therefore, the dimension of the square based prism is:
2cm x 2cm x 15cm
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