Respuesta :
Answer:
The width is 5m and the length is 10m.
Step-by-step explanation:
Rectangle:
Has two dimensions: Width(w) and length(l).
It's area is:
[tex]A = w*l[/tex]
The length of a rectangle is 5m less than three times the width
This means that [tex]l = 3w - 5[/tex]
The area of the rectangle is 50m^(2)
This means that [tex]A = 50[/tex]. So
[tex]A = w*l[/tex]
[tex]50 = w*(3w - 5)[/tex]
[tex]3w^{2} - 5w - 50 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]3w^{2} - 5w - 50 = 0[/tex]
So
[tex]a = 3, b = -5, c = -50[/tex]
[tex]\bigtriangleup = (-5)^{2} - 4*3*(-50) = 625[/tex]
[tex]w_{1} = \frac{-(-5) + \sqrt{625}}{2*3} = 5[/tex]
[tex]w_{2} = \frac{-(-5) - \sqrt{625}}{2*3} = -3.33[/tex]
Dimension must be positive result, so
The width is 5m(in meters because the area is in square meters).
Length:
[tex]l = 3w - 5 = 3*5 - 5 = 10[/tex]
The length is 10 meters
