Answer :
Answer:
[tex]Length =95[/tex] feet
[tex]width =75[/tex] feet
Step-by-step explanation:
Let x be the width of a rectangle
Let l be the length of a rectangle
Let A be the area of rectangle
Given.
The garden is 20 feet longer than wide
therefore [tex]l=20+w=20+x[/tex]
Area of rectangle is [tex]7125[/tex]
We know that area of rectangle is
[tex]A = l\times w[/tex]---------------------(1)
put all known values in equation 1
[tex]7125 = (20+x)\times x[/tex]
[tex]x^{2} +20x-7125=0[/tex]
Find roots of equation by this formula
where [tex]a=1, b=20, c=-7125[/tex]
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x=\frac{-20\pm\sqrt{20^{2}-4(1)(-7125) } }{2(1)}[/tex]
[tex]x=\frac{-20\pm\sqrt{28900 } }{2}[/tex]
[tex]x=75[/tex] or [tex]x=-95[/tex]
check both value in equation 1
[tex]A=(20+75)\times 75\\A=7125[/tex]
So, the [tex]x=75[/tex] is satisfy the equation 1.
So The length of rectangle = [tex]20+x[/tex] = [tex]20+75[/tex] = [tex]95[/tex] feet
And width is 75 feet