Question 98129
The length of a rectangle is 2 cm more than 3 times its width. If the
area of the rectangle is 95 cm2, find the dimensions of the rectangle.
:
Let x = width of the rectangle
:
It says,"The length of a rectangle is 2 cm more than 3 times its width." Therefore
Length = (3x + 2)
:
"area of the rectangle is 95 cm2,"
  L * W = 95
Therefore:
(3x+2) * x = 95
:
3x^2 + 2x = 95
:
3x^2 + 2x - 95 = 0; a quadratic equation, solve using the quadratic formula
a = 3; b = 2; c = -95
:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{x = (-2 +- sqrt( 2^2 - 4 * 3 * -95 ))/(2*3) }}}
:
{{{x = (-2 +- sqrt(4 - (-1140) ))/(6) }}}
:
{{{x = (-2 +- sqrt(4 + 1140 ))/(6) }}}; minus a minus is a plus
:
{{{x = (-2 +- sqrt(1144 ))/(6) }}}
Two solutions, but it's the positive solution we want here
{{{x = (-2 + 33.823)/6}}}
{{{x = 31.823/6}}}
x = 5.305 is the width
:
Length = 3(5.305) + 2 = 17.915 is the length
:
:
Check solution:
5.305 * 17.915 = 95.0