Question 942348
the height is equal to 24.8 rounded to the nearest tenth.


you have 2 equations:


from the standard size screen, you get x^2 + (x+3)^2 = y^2


from the wide screen, you get x^2 + (1.9x)^2 = (y+16)^2


from the second equation, you solve for y^2 to get y^2 = (sqrt(4.61x^2) - 16)^2


you can then substitute for y^2 in the first equation to get:


x^2 + (x+3)^2 = (sqrt(4.61x^2) - 16)^2


you then simplify to get:


x^2 + x^2 + 6x + 9 = 4.61x^2 - 32*sqrt(4.61x^2) + 256


you then simplify further to get:


2x^2 + 6x + 9 = 4.61x^2 - 32*sqrt(4.61)*x + 256


you then simplify further to get:


2x^2 + 6x + 9 = 4.61x^2 - 68.70691377x + 256


you then subtract (2x^2 + 6x + 9) from both sides of the equation to get:


0 = 4.61x^2 - 2x^2 - 68.70691377x - 6x + 256 - 9


you then combine like terms to get:


0 = 2.61x^2 - 74.70691377x + 247.


this is a quadratic equation that is in standard form.


you get:


a = 2.61
b = -74.70691377
c = 247


you use the quadratic formula to get:


x = 24.80870998 or x = 3.814628628.


you then place both values in the original equations to see if they're true.


x = 3.814628628 doesn't work so it's extraneous and is discarded.


x = 24.80870998 works so that's your solution.


when x = 24.80870998:


y = square root of (x^2 + (x+3)^2) = 37.2665593 and (y+16) = square root of (x^2 + (1.9x)^2) = 53.2665593.


the difference between them is 16 per the requirements of the problem.


round to the nearest tenth and 24.8 is your solution.