SOLUTION: A rectangular window has decorative trim that goes across the diagonals. Each piece of diagonal trim measures 53 inches, and the length of the window is 17 inches more than the wid

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rectangular window has decorative trim that goes across the diagonals. Each piece of diagonal trim measures 53 inches, and the length of the window is 17 inches more than the wid      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1063212: A rectangular window has decorative trim that goes across the diagonals. Each piece of diagonal trim measures 53 inches, and the length of the window is 17 inches more than the width. What are the dimensions of the window?
A) write and equation to help you solve the problem.
B) solve the equation and write the answer is in appropriate units
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
width is x
length is x+17
diagonal is 53
Pythagorean theorem
x^2+(x+17)^2=53^2
x^2+x^2+34x+289=2809
2x^2+34x-2520=0
divide by 2
x^2+17x-1260=0
x=(1/2)(-17+/- sqrt (289+1260*4)); sqrt (5329)=73
only positive root is (1/2)(-17+73)=28 in--that is the width and its square is 784
length is 45 in, square is 2025
They sum to 2809