Question 80995
The length of a rectangle is 5 cm more than 3 times its width. If the area of the rectangle is 95 cm^2, find the dimensions of the rectangle to the nearest thousandth.

ANSWER:

Assume that width of the rectangle is 'x' cm.

Then 3 times width = 3x


5 cm more than 3 times its width = (3x + 5)cm


It is given that its length is 5cm more than 3 times its width

So length of the rectangle = (3x + 5) cm.


Area of a rectangle is given by the formula, A = length * width


Here area is given that 95 cm^2



So we can write it as,


90 = (3x + 5 ) * x


==> 95 = 3x * x + 5 * x

==> 95 = 3x^2 + 5x


Subtract 95 from both sides of the equation, then we will obtain a quadratic equation.


==> 95 - 95 = 3x^2 + 5x - 95


==> 0 = 3x^2 + 5x - 95



3x^2 + 5x - 95 = 0


We can solve this equation using quadratic formula.


standard form of a quadratic equation is,


ax^2 + bx + c = 0 ---------------(2)


By quadratic formula, the solution is given by,



{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a)}}}


Comparing (1) and (2) we have,


a = 3, b = 5 and c = -95



so the solution is,


{{{x = (-5 +- sqrt( 5^2-4*3*(-95) ))/(2*3)}}}



{{{x = (-5 +- sqrt( 25 + 1140 ))/(6)}}}



{{{x = (-5 +- sqrt( 1165 ))/(6)}}}



{{{x = (-5 +- 34.13)/6}}}


x = (-4 + 34.14)/6 or x = (-4 - 34.13 )/6


x = 30.14/6 or x = -38.13/6


( since negative values are not admisible here)


==> x = 5.023 cm


So width of the rectangle is 5.023 cm.


so width = 5.023 cm.

and length = 3x + 5 = 3 * (5.782) + 5 = 15.069 + 5 = 20.069 cm


So the dimenstions of the given rectangle:

length = 20.069 cm and

Width = 5.023 cm.

To check your answer, multiply length with breadth, then you will get 95 approximately.



Hope you understood.

Regards.


Praseena.