SOLUTION: If the sides of a rectangle have lengths 7 and 12, find the length of a diagonal to the nearest tenth.

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Question 177147: If the sides of a rectangle have lengths 7 and 12, find the length of a diagonal to the nearest tenth.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If we divide the rectangle in half along the diagonal, we get the following triangle:





Since the legs are 7 and 12 this means that a=7 and b=12


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


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


7%5E2%2B12%5E2=x%5E2 Plug in a=7, b=12, c=x


49%2B12%5E2=x%5E2 Square 7 to get 49.


49%2B144=x%5E2 Square 12 to get 144.


193=x%5E2 Combine like terms.


x%5E2=193 Rearrange the equation.


x=sqrt%28193%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=13.892 Approximate the square root with a calculator.


x=13.9 Round to the nearest tenth.


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Answer:


So the length of the diagonal is approximately 13.9 units.