SOLUTION: Toshiba is working on a 50-inch diagnol measure television that has a height that is 24 inches less than the length. What are the dimensions of the rectangular screen? I have go

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Question 194157: Toshiba is working on a 50-inch diagnol measure television that has a height that is 24 inches less than the length. What are the dimensions of the rectangular screen?
I have gotten through most steps to get an equation of x^2 - 24x - 962=0 and am having a very hard time factoring that. Please help!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Toshiba is working on a 50-inch diagonal measure television that has a height
that is 24 inches less than the length.
What are the dimensions of the rectangular screen?
:
:
I think you made a small mistake here
:
Let x = the height
then
(x+24) = the width
:
x^2 + (x+24)^2 = 50^2
:
x^2 + x^2 + 48x + 576 = 2500
:
2x^2 + 48x + 576 - 2500 = 0
:
2x^2 + 48x - 1924 = 0
Simplify divide by 2
x^2 + 24x - 962 = 0; 24x is positive
;
Using the quadratic formula, I got x = 21.25" (the height
then the width: 45.25"
:
Check solution on calc: enter sqrt%2821.25%5E2+%2B+45.25%5E2%29 = 49.99 ~ 50
:
you did not make a mistake, if you made x = the width, then the height = (x-24)
The quadratic equation you had was correct, but it will not factor. using
the quadratic formula you would get x = 45.25 which is right. Sorry I missed that. Carl