SOLUTION: What is the length of the diagonal of a rectangle with width 8 cm and length 6 cm

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Question 481965: What is the length of the diagonal of a rectangle with width 8 cm and length 6
cm
Found 2 solutions by jim_thompson5910, ewatrrr:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are 8 and 6 this means that a=8 and b=6


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


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


8%5E2%2B6%5E2=x%5E2 Plug in a=8, b=6, c=x


64%2B6%5E2=x%5E2 Square 8 to get 64.


64%2B36=x%5E2 Square 6 to get 36.


100=x%5E2 Combine like terms.


x%5E2=100 Rearrange the equation.


x=sqrt%28100%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=10 Simplify the square root.


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Answer:


So the solution is x=10.


So the length of the diagonal is 10 cm.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Re Pythagorean Theorem

 diagonal = sqrt(8cm^2 + 6cm^2) = 10cm