Respuesta :
Dimensions are length 20 meter and width 14 meter
Solution:
Let "a" be the length of rectangle
Let "b" be the width of rectangle
Given that,
A rectangle has width that is 6 meters less than the length
Width = length - 6
b = a - 6
The area of the rectangle is 280 square meters
The area of the rectangle is given by formula:
[tex]Area = length \times width[/tex]
Substituting the values we get,
[tex]Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0[/tex]
Solve the above equation by quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}[/tex]
[tex]a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14[/tex]
Since, length cannot be negative, ignore a = -14
Thus solution of length is a = 20
Therefore,
width = length - 6
width = 20 - 6 = 14
Thus dimensions are length 20 meter and width 14 meter
