Question

Un jardín rectangular de 50 cm de largo por 34 m de ancho está rodeado por un camino de arena uniforme.Halla la anchura de dicho camino si se sabe que su área es de 540m2

Answer 1

5.85 m

Explanation:

The width of the sand road can be calculated knowing its area and the dimensions of the rectangular garden as follows:

`A_(g) = a.b`

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

`A_(s) = 540 m^(2)`

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:

`A_(s) + A_(g) = (a+2x)*(b+2x)`

`540 m^(2) + 0.5m*34m = ab + 2ax + 2bx + 4x^(2)`

`557 m^(2) = ab + 2x(a + b) + 4x^(2)`

`557 m^(2) - 17m^(2) - 2x(34.5 m) - 4x^(2) = 0`

`540 - 69x - 4x^(2) = 0`

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!