Question 60812
Hi ac,
The length of a rectangle is 5 cm more than 2 times its width.  If the area of the rectangle is 78cm^2, find the dimensions of the rectangle to the nearest thousandth.
:
Let the width be: x
Then the length is: 2x+5
Area is: 78 cm^2
Area=length*width
:
78=x(2x+5)
78=2x^2+5x
0=2x^2+5x-78
This is in standard form:{{{ax^2+bx+c=0}}}
We can use the quadratic formula to solve it:{{{highlight(x=(-b+-sqrt(b^2-4*a*c))/(2*a))}}}
a=2, b=5, and c=-78
{{{x=(-5+-sqrt(5^2-4(2)(-78)))/(2(2))}}}
{{{x=(-5+-sqrt(25+624))/4}}}
{{{x=(-5+-sqrt(649))/4}}}
You can ignore the negative dimension.
x=5.119
The width is: x=5.119 cm
Length is:2x+5=2(5.119)+5=15.238 cm
Happy Calculating!!!