Answer:
5.85 m
Step-by-step explanation:
The width of the sand road can be calculated knowing its area and the dimensions of the rectangular garden as follows:
[tex] A_{g} = a.b [/tex]
Where:
Ag: is the area of the rectangular garden
a: is the length of the rectangular garden = 50 cm = 0.5 m
b: is the width of the rectangular garden = 34 m
[tex] A_{s} = 540 m^{2} [/tex]
Where:
As: is the area of the sand road
The relation between the area of the sand road and the area of the rectangular garden is the following:
[tex] A_{s} + A_{g} = (a+2x)*(b+2x) [/tex]
[tex] 540 m^{2} + 0.5m*34m = ab + 2ax + 2bx + 4x^{2} [/tex]
[tex] 557 m^{2} = ab + 2x(a + b) + 4x^{2} [/tex]
[tex] 557 m^{2} - 17m^{2} - 2x(34.5 m) - 4x^{2} = 0 [/tex]
[tex] 540 - 69x - 4x^{2} = 0 [/tex]
By solving the above equation for x we have two solutions:
x₁ = -23.10 m
x₂ = 5.85 m
Taking the positive value, we have that the width of the sand road is 5.85 m.
I hope it helps you!
