SOLUTION: TV's are measured by the length of their diagonals. The ratio of a TV's length to width is 4:3 and its size is 55 inches. What is the perimeter around the TV?

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Question 1047690: TV's are measured by the length of their diagonals. The ratio of a TV's length to width is 4:3 and its size is 55 inches. What is the perimeter around the TV?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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%5E2+%2B+b%5E2+=+c%5E2
%284x%29%5E2+%2B+%283x%29%5E2+=+55%5E2
16x%5E2%2B9x%5E2+=+3025
25x%5E2+=+3025
%2825x%5E2%29%2F25+=+3025%2F25
x%5E2+=+121
sqrt%28x%5E2%29+=+sqrt%28121%29
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 154 inches