Answer:
Part 1) An expression for the area of the inner square is [tex]x^{2}=0.75(20)^{2}[/tex]
Part 2) The area of the entire garden is [tex]400\ ft^{2}[/tex]
Part 3) 75% of the area of the entire garden is [tex]300\ ft^{2}[/tex]
Part 4) The equation is [tex]x^{2}=300[/tex]
Part 5) The solutions of the quadratic equation are [tex]x=(+/-)17.3\ ft[/tex]
Part 6) The solution that best describes the side length of the inner square is [tex]x=17.3\ ft[/tex]
Step-by-step explanation:
Part 1) What is an expression for the area of the inner square?
we know that
The area of the inner square is equal to
[tex]A=x^{2}[/tex]
[tex]A=0.75(20)^{2}[/tex]
so
[tex]x^{2}=0.75(20)^{2}[/tex]
Part 2) What is the area of the entire garden?
The area of the entire garden is
[tex](20)^{2}=400\ ft^{2}[/tex]
Part 3) What is 75% of the area of the entire garden?
we know that
[tex]75\%=75/100=0.75[/tex]
so
[tex]0.75*(400)=300\ ft^{2}[/tex]
Part 4) Write an equation for the area of the inner square using the expressions from Steps 1 and 3
[tex]x^{2}=0.75(20)^{2}[/tex]
[tex]x^{2}=300[/tex]
Part 5) Solve the quadratic equation. Round to the nearest tenth of a foot
we have
[tex]x^{2}=300[/tex]
square root both sides
[tex]x=(+/-)\sqrt{300}[/tex]
[tex]x=(+/-)17.3\ ft[/tex]
Part 6) Which solution to the quadratic equation best describes the side length of the inner square?
[tex]x=(+/-)17.3\ ft[/tex]
so
The solution that best describes the side length of the inner square is
[tex]x=17.3\ ft[/tex]
because
The side length can not be a negative number
