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
Question
Answer:
the correct question isThe 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
solved
general
11 months ago
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