Question 91542
Question:


Mr.Jon's garden covered 300 square feet. If the width was 5 feet less than the length, find the measurements of the garden.



Answer:

Area of the garden = 300 square feet.


Assume that  length = 'x' feet


Then width = x - 5 feet


Area = length * width


that is...

300 = x * (x -5 )


==> {{{300 = x^2 - 5x}}}


Subtract 300 from both sides....


==> {{{300 - 300  = x^2 - 5x - 300}}}


==> {{{0 = x^2 - 5x - 300 }}}, which is  a quadratic equation...

You can solve it   using quadratic formula


{{{x = (-(-5) +- sqrt( (-5)^2-4*1*(-300) ))/(2*1) }}}


{{{x =((5) +- sqrt( 1225))/(2) }}}


==> {{{x =((5) +- 35)/2 }}}


==> {{{x =((5)  + 35)/2 }}}  or   {{{x =((5)  - 35)/2 }}}



==> {{{x =(40)/2 }}}  or   {{{x =-30/2 }}}



==> {{{x =20}}}  or   {{{x = -15 }}}


Hence the value of x


That is length = 20 feet   or 15feet


Measurements:

When length = 20 feet, width = 20 - 5 = 15 feet


When length = -15 feet, width = -15 -5 = -20 feet.


Hope you found the explanation useful.


Regards.

Praseena.