SOLUTION: Television screens are usually measured by the length of its diagonal. The television set has a 60 – inch diagonal. the screen is 12 inches wider than its height. Find the dimen

Algebra ->  Test -> SOLUTION: Television screens are usually measured by the length of its diagonal. The television set has a 60 – inch diagonal. the screen is 12 inches wider than its height. Find the dimen      Log On


   

Question 979838: Television screens are usually measured by the length of its
diagonal. The television set has a 60 – inch diagonal. the
screen is 12 inches wider than its height. Find the
dimensions of the screen. THANKS IN ADVANCE
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x, width
y, height
diagonal is a hypotenuse of right triangle with legs x and y.

12%2By=x, and x, are the legs.
x%5E2%2By%5E2=60%5E2-----Pythagorean Theorem, because Right Triangle;
%2812%2By%29%5E2%2By%5E2=60%5E2
144%2B24y%2By%5E2%2By%5E2=3600
2y%5E2%2B24y%2B144=3600
y%5E2%2B12y%2B72=1800
y%5E2%2B12y%2B72-1800=0
y%5E2%2B12y-1728=0

You can factorize the constant nonvariable term.
12*12*12=2*...... but if you don't want to check all of that, use discriminant.
%2812%29%5E2-4%2A%28-1728%29=144%2B4%2A1728=7056=84%5E2.

y=%28-12%2B84%29%2F2, based on formula for general solution to quadratic equation, jumping through a couple of steps.
highlight%28y=36%29.

Now find x.
x=12%2By
x=12%2B36
highlight%28x=48%29.