Respuesta :
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[tex]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:
A = w*lA=w∗l
The length of a rectangle is 5m less than three times the width
This means that l = 3w - 5l=3w−5
The area of the rectangle is 50m^(2)
This means that A = 50A=50 . So
A = w*lA=w∗l
50 = w*(3w - 5)50=w∗(3w−5)
3w^{2} - 5w - 50 = 03w2−5w−50=0
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
ax^{2} + bx + c, a\neq0ax2+bx+c,a=0 .
This polynomial has roots x_{1}, x_{2}x1,x2 such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})ax2+bx+c=a(x−x1)∗(x−x2) , given by the following formulas:
x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}x1=2∗a−b+△
x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}x2=2∗a−b−△
\bigtriangleup = b^{2} - 4ac△=b2−4ac
In this question:
3w^{2} - 5w - 50 = 03w2−5w−50=0
So
a = 3, b = -5, c = -50a=3,b=−5,c=−50
\bigtriangleup = (-5)^{2} - 4*3*(-50) = 625△=(−5)2−4∗3∗(−50)=625
w_{1} = \frac{-(-5) + \sqrt{625}}{2*3} = 5w1=2∗3−(−5)+625=5
w_{2} = \frac{-(-5) - \sqrt{625}}{2*3} = -3.33w2=2∗3−(−5)−625=−3.33
Dimension must be positive result, so
The width is 5m(in meters because the area is in square meters).
Length:
l = 3w - 5 = 3*5 - 5 = 10l=3w−5=3∗5−5=10
The length is 10 meters
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