Sign Up FREE!  Sign In  Classroom Setup  Common Core Alignment  
07162010  #1 
Join Date: Jul 2010
Posts: 1

Help! Fiding dimentions from an equation.
I need some help figuring out how to find the dimensions to this question:
A rectangle has perimeter 64cm and area 23cm^2. Solve the following system of equations to find the rectangle's dimensions. a) l = 23/w l + w = 32 b) solve the system of equations x^2 + y^2 = 1 xy = 0.5 Please and thank you! I know the answer, I just don't know how to do the question. 
07212010  #2 
Join Date: Mar 2005
Posts: 10,648

l = 23/w
l + w = 32 23/w + w = 32 23 + w^2 = 32w w^2  32w + 23 = 0 Use the quadratic formula to solve for w: w = 31.264 and 0.73566. l = 1.35930435 and 0.0319852174.
__________________
Do Math and you can do Anything! 
07262010  #3  
Join Date: Dec 2008
Posts: 249

Quote:
Since xy = 0.5 then x = 1/(2y) Substituting for x gives: (1/(2y))^2 + y^2 = 1 1/(4y^2) + y^2 = 1 (1 + 4y^4)/(4y^2) = 1 1 + 4y^4 = 4y^2 4y^4  4y^2 + 1 = 0 y^4  y^2 + 1/4 = 0 (y^2  1/2)(y^2  1/2) = 0 y^2  1/2 = 0 y^2 = 1/2 y = + or  sqrt(1/2) x = + or  sqrt(1/2) 

Thread Tools  
Display Modes  

