Respuesta :
[tex](x + 8)( x + 6) = 400 \\ x { }^{2} + 14x - 352 = 0 \\ (x + 7) {}^{2} - 401 = 0 \\ x = - 7 + \sqrt{401} \\ [/tex]
Length of the rectangular patio = (x + 6) m
width of the rectangular patio = (x +8)m
Area of rectangle=Length*Width.
400=(x+6)(x+8)
400=[tex] x^{2} [/tex]+14x+48
For completing square, first add - 48 on both side
400 - 48 = [tex] x^{2} [/tex]+14x
352 = [tex] x^{2} [/tex]+14x
To make a complete square add the third term =[tex] \left ( \frac{-b}{2a} \right )^{}2 [/tex]
a= 1 and b= 14
Third term = [tex] \left ( \frac{-14}{2} \right )^{}2 [/tex]
Third term = 49
Now add 49 in both side of the equation
352 + 49 = [tex] x^{2} [/tex]+14x + 49
401 = [tex] \left ( x+7 \right )^{2} [/tex]
Taking square root on both sides
[tex] x + 7 = \pm \sqrt{401} [/tex]
We can not consider the negative value
so x + 7 = 20.02
x = 20.02 -7
x= 13.02
Length of the rectangular patio = (x + 6) = 13.02 + 6 = 19.02 m
width of the rectangular patio = (x +8) = 13.02 + 8 = 21.02 m
