SOLUTION: A rectangle is 7 cm wide and 10 cm long. Find the length diagonal of the rectangle

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Question 130100: A rectangle is 7 cm wide and 10 cm long. Find the length diagonal of the rectangle
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

If we cut the rectangle in two equal halves along the diagonal, we basically have this triangle set up:

drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2C7%29%2C%0D%0Alocate%281%2C-0.2%2C10%29%2C%0D%0Alocate%281%2C2%2Cx%29%0D%0A%29
Since we can see that the triangle has legs of 7 and 10 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



7%5E2%2B10%5E2=x%5E2 Plug in a=7, b=10, and c=x. Now lets solve for x


4+9+%2B+1+0+0+=++x++%5E+2 Square each individual term



1+4+9+=++x++%5E+2 Combine like terms


s+q+r+t+%28+1+4+9+%29+=+s+q+r+t+%28++x++%5E+2+%29 Take the square root of both sides


Which approximates to...

12.2065556157337=x

So our answer is
x=12.2065556157337