Question 196285
Well, I hope I'm in time to rescue your sanity. (lol)

1) The size of a TV is designated by the length of the screen's diagonal.
A 10" TV then has a diagonal of 10".
If the width of a 10" TV is 8", its height can be found by using the Pythagorean theorem: {{{c^2 = a^2+b^2}}} and in this case, c (the diagonal) is 10" and a is 8", so b would be the height of the TV.
{{{c^2 = a^2+b^2}}} Substitute c = 10, a = 8, and solve for b, the height.
{{{10^2 = 8^2 + b^2}}}
{{{100 = 64+b^2}}} Subtract 64 from both sides of the equation.
{{{36 = b^2}}} Take the square root of both sides.
{{{b = 6}}} or {{{b = -6}}} Discard the negative solution as the height can only be a positive value.
The height of the TV is 6"
2) Start with the formula for the perimeter of a rectangle: {{{A = 2(L+W)}}} where L = length and W = width.In this problem, L = x+6 and W = x, so...
{{{P = 2((x+6)+(x))}}} Expand.
{{{P = 2(2x+6)}}} Distribute the 2.
{{{highlight(P = 4x+12)}}}