SOLUTION: Two television monitors sitting beside each other on a shelf in an appliance store have the same screen height. One has a conventional screen, which is 7 inches wider than it is hi

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Two television monitors sitting beside each other on a shelf in an appliance store have the same screen height. One has a conventional screen, which is 7 inches wider than it is hi      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 178251: Two television monitors sitting beside each other on a shelf in an appliance store have the same screen height. One has a conventional screen, which is 7 inches wider than it is high. The other has a wider, high-definition screen, which is 1.8 times as wide as it is high. The diagonal measure of the wider screen is 17 inches more than the diagonal measure of the smaller. What is the height of the screens, correct to the nearest 0.1 inch?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two television monitors sitting beside each other on a shelf in an appliance store have the same screen height. One has a conventional screen, which is 7 inches wider than it is high. The other has a wider, high-definition screen, which is 1.8 times as wide as it is high. The diagonal measure of the wider screen is 17 inches more than the diagonal measure of the smaller. What is the height of the screens, correct to the nearest 0.1 inch?
:
Let x = height of both screens:
:
Conventional screen dimensions: (x+7) by x
HD screen dimensions: 1.8x by x
:
Find x by writing an equation of the diagonals (hypotenuse) of the screens
HD diagonal = Conventional diagonal + 17 inches
sqrt%28x%5E2+%2B+%281.8x%29%5E2%29 = sqrt%28x%5E2+%2B+%28x%2B7%29%5E2%29 + 17
:
sqrt%28x%5E2+%2B+3.24x%5E2%29 = sqrt%28x%5E2+%2B+%28x%5E2%2B14x%2B49%29%29 + 17
:
sqrt%284.24x%5E2%29 - sqrt%282x%5E2%2B14x%2B49%29%29 - 17 = 0
To avoid a tremendous amt of math, graph this equation:

:
Note the positive intercept occurs at x~34" or 34.4" on a Ti83
:
Check solution by finding the diagonals using x = 34.4
HD sqrt%2834.4%5E2+%2B+%281.8%2A34.4%29%5E2%29 = 70.8
Convent sqrt%2834.4%5E2+%2B+41.4%5E2%29 = 53.8
------------------------------------------
This will give us a difference of: 17.0"
:
:
I'll let you find the actual width of the two screens: