Answer:
The width of the garden is 1.16 m
Step-by-step explanation:
step 1
Find the area of the garden
To find out the area of the garden multiply by 1/3 the area of the building
[tex]225(\frac{1}{3})=75\ m^2[/tex]
step 2
Find the length side of the square building
The area of a square is
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]A=225\ m^2[/tex]
so
[tex]b^2=225\\b=15\ m[/tex]
step 3
Find the width of the garden
Let
x ----> the width of the garden
we know that
The area of the building plus the area of the garden is equal to
[tex](15+2x)^2=225+75[/tex]
solve for x
[tex]225+60x+4x^2=225+75\\4x^2+60x-75=0[/tex]
Solve the quadratic equation by graphing
using a graphing tool
The solution is x=1.16 m
see the attached figure
therefore
The width of the garden is 1.16 m
Find the exact value
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]4x^2+60x-75=0[/tex]
so
[tex]a=4\\b=60\\c=-75[/tex]
substitute in the formula
[tex]x=\frac{-60\pm\sqrt{60^{2}-4(4)(-75)}} {2(4)}[/tex]
[tex]x=\frac{-60\pm\sqrt{4,800}} {8}[/tex]
[tex]x=\frac{-60\pm40\sqrt{3}} {8}[/tex]
[tex]x=\frac{-60+40\sqrt{3}} {8}\ m[/tex] ----> exact value
