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

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) (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 and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , ,

Square to get .

Square to get .

Combine like terms.

Rearrange the equation.

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

Simplify the square root.

Use your calculator to evaluate and simplify

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Answer:

So the solution is approximately 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 and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , ,

Square to get .

Square to get .

Combine like terms.

Rearrange the equation.

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

Simplify the square root.

Evaluate the square root of 41 and multiply

Now round down (to the nearest inch) to get

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
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