SOLUTION: 6) If the sides of a dinning room are 21 feet by 18 feet, what is the length of the diagonal? 7) I have 60 inches of width and have 48 inches of height in my entertainment

Algebra ->  Pythagorean-theorem -> SOLUTION: 6) If the sides of a dinning room are 21 feet by 18 feet, what is the length of the diagonal? 7) I have 60 inches of width and have 48 inches of height in my entertainment      Log On


   

Question 180259: 6) If the sides of a dinning room are 21 feet by 18 feet, what is the length of the diagonal?

7) I have 60 inches of width and have 48 inches of height in my entertainment center. I am going HDTV shopping, what is the biggest diagonal TV that I can get?

** I don't know if i'm in the right category, but thanks a million.**
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6)



If we cut the table along the diagonal, we'll have this triangle set up:





Since the legs are 18 and 21 this means that a=18 and b=21


Also, since the hypotenuse is x, this means that c=x.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


18%5E2%2B21%5E2=x%5E2 Plug in a=18, b=21, c=x


324%2B21%5E2=x%5E2 Square 18 to get 324.


324%2B441=x%5E2 Square 21 to get 441.


765=x%5E2 Combine like terms.


x%5E2=765 Rearrange the equation.


x=sqrt%28765%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=3%2Asqrt%2885%29 Simplify the square root.


x=27.659 Use your calculator to evaluate and simplify


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Answer:


So the solution is approximately x=27.659 which means that the diagonal is about 27.659 feet






7)


Again, if we cut the TV in half along the diagonal we'll have this triangle set up:





Since the legs are 48 and 60 this means that a=48 and b=60


Also, since the hypotenuse is x, this means that c=x.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


48%5E2%2B60%5E2=x%5E2 Plug in a=48, b=60, c=x


2304%2B60%5E2=x%5E2 Square 48 to get 2304.


2304%2B3600=x%5E2 Square 60 to get 3600.


5904=x%5E2 Combine like terms.


x%5E2=5904 Rearrange the equation.


x=sqrt%285904%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=12%2Asqrt%2841%29 Simplify the square root.


x=76.837 Evaluate the square root of 41 and multiply


Now round down (to the nearest inch) to get x=76


So this tells us that the largest diagonal TV would be 76 inches


Note: you can ignore rounding, but keep in mind that the ".837" portion would need to be converted