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Answer:
The width of the garden is 22.12 m and its length is 27.12 m
Step-by-step explanation:
Equations
Let x = width of the garden
The length is 5 m longer than the wide, thus:
x + 5 = length of the garden
The area of the rectangular garden is
A=x(x+5)=600
Operating:
[tex]x^2+5x-600=0[/tex]
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Where a=1 b=5 c=-600:
[tex]\displaystyle x=\frac{-5\pm \sqrt{5^2-4(1)(-600)}}{2(1)}[/tex]
Operating:
[tex]\displaystyle x=\frac{-5\pm \sqrt{25+2400}}{2}[/tex]
[tex]\displaystyle x=\frac{-5\pm \sqrt{2425}}{2}[/tex]
There are two solutions:
x = 22.12
x = -27.12
The negative solution is not valid because x is the width of the garden, thus
x = 22.12 m
And
y = 22.12 + 5 = 27.12 m
The width of the garden is 22.12 m and its length is 27.12 m