Question 172425
Question:

The length of a rectangle is 4 cm more than 3 times its width.  If the area of the rectangle is 95 cm2, find the dimensions of the rectangle to the nearest thousandth.

Answer:

Area of a rectangle is given by the formula,

A = length * width

Given, A = {{{ 95 cm^2}}}

length = 4 cm more than 3 times its width


Let us assume that width = x cm


==> length = 3x + 4 (because, length = 4 cm more than 3 times its width)



so... area = length * width  = (3x + 4) * x

 95 = (3x + 4) * x

==> 95 = 3x*x  + 4* x


==> {{{ 95 = 3x^2 + 4x }}}



==> {{{ 3x^2 + 4x - 95 = 0}}}
this is a quadratic equation, you can solve it using quadratic formula

==> {{{x = (-4 +- sqrt( (-4)^2-4*3*(-95) ))/(2*3) }}} 
==> {{{x = (-4 +- sqrt( 16 + 1140 ))/(6) }}} 

==> {{{x = (-4 +- sqrt( 1156 ))/(6) }}} 


==> {{{x = (-4 +- 34)/(6) }}} 


==> {{{x = (-4 + 34)/(6) }}}  or  {{{x = (-4 - 34)/(6) }}}


 ==> {{{x = (30)/(6) }}}  or  {{{x = (-38)/(6) }}}



 ==> {{{x = 5 }}}  or  {{{x = -6.333 }}}

here u can take the value x= 5 since negative value cant be a length measure


so width = 5 cm


and length = 3*5 + 4 = 15 + 4 = 19



so the dimensions are 19 cm and 5cm


hence the answer.


hope u found it useful.


Regards.


Praseena