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The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot

1 Answer

4 votes
the correct question is
The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot. The base of the rectangular prism is not a square and the width is greater than 2 feet. What is the length and width of the rectangular prism?

let
x-------> the length of the base of the rectangular prism
y-------> the width of the base of the rectangular prism

we know that
volume of the prism=area of the base*height
volume=48 ft
³
height of the prism=3/4 ft

area of the base=volume/height--------> 48/(3/4)---> 48*4/3----> 64 ft
²

area of the base=64 ft
²
area of the base=x*y
64=x*y--------> equation 1

y=x+2--------> equation 2

substitute equation 2 in equation 1
64=x*[x+2]-----> 64=x
²+2x------> x²+2x-64=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
x=7.062 ft
y=x+2-----> y=7.062+2-----> y=9.062 ft

the answer is
the length of the base of the rectangular prism is 7.062 ft
the width of the base of the rectangular prism is 9.062 ft
The raised vegetable garden in Susan's yard is in the shape of a rectangular prism-example-1
answered
User Translunar
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