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.
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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 ft³ height of the prism=3/4 ft
area of the base=volume/height--------> 48/(3/4)---> 48*4/3----> 64 ft² area of the base=64 ft² 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=x²+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
