SOLUTION: Please show all work. Thanks in advance. Solving using a system of two equations and two unknowns. A computer parts company wants to make a rectangle memory board that has

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please show all work. Thanks in advance. Solving using a system of two equations and two unknowns. A computer parts company wants to make a rectangle memory board that has       Log On


   

Question 602129: Please show all work. Thanks in advance.
Solving using a system of two equations and two unknowns.
A computer parts company wants to make a rectangle memory board that has a perimeter of 34cm and a diagonally of length 13cm. Find the dimensions of a board. Consider the length to be the longer side.


Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
le length be x
width be y
perimeter = 2(x+y) = 34
/2
x+y =17
By Pythagoras theorem
The doagonal forms a right triangle with the sides
x%5E2%2By%5E2=+13%5E2
add 2xy
x%5E2%2B2xy%2By%5E2=169%2B2xy

%28x%2By%29%5E2=169%2B2xy
17^2=169+2xy
289=169%2B2xy
289-169=2xy
120=2xy
xy = 60
x= 60/y

x+y =17
60/y + y = 17
60+y^2=17y
y^2-17y+60=0
y^2-12y-5y+60=0
y(y-12)-5(y-12)=0
(y-12)(y-5)=0
y= 12cm OR 5cm
The dimensions are 12cm length & 5 cm width