Question 1047690
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The ratio is 4:3 which means the width is 4x and the height is 3x where x is some positive number


Draw the diagonal on the rectangular tv image. You'll see a right triangle forming. 


The legs of this triangle are 4x and 3x. The hypotenuse is 55. So,
a = 4x
b = 3x
c = 55


Let's use the pythagorean theorem to solve for x.


{{{a^2 + b^2 = c^2}}}
{{{(4x)^2 + (3x)^2 = 55^2}}}
{{{16x^2+9x^2 = 3025}}}
{{{25x^2 = 3025}}}
{{{(25x^2)/25 = 3025/25}}}
{{{x^2 = 121}}}
{{{sqrt(x^2) = sqrt(121)}}}
{{{x = 11}}} or {{{x = -11}}}
Ignore the negative x value. Recall that x must be positive.


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So we know that x = 11 now. Let's use this to find the width and height


width = 4*x = 4*11 = 44
height = 3*x = 3*11 = 33


This tv has a width of 44 inches (horizontal) and height of 33 inches (vertical)


Add up all the sides of the rectangle to get: 44+33+44+33 = 154


The perimeter is <font color=red size=5>154 inches</font>
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