SOLUTION: A rectangle has side length 30 mm and diagonal length 34 mm. Find the length of the other side of the rectangle to the nearest whole number.

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: A rectangle has side length 30 mm and diagonal length 34 mm. Find the length of the other side of the rectangle to the nearest whole number.      Log On

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Question 176435This question is from textbook
: A rectangle has side length 30 mm and diagonal length 34 mm. Find the length of the other side of the rectangle to the nearest whole number.This question is from textbook

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
If we cut the rectangle in half along the diagonal, we get the following triangle:

drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%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%2Cx%29%2C%0D%0Alocate%281%2C-0.2%2C30%29%2C%0D%0Alocate%281%2C2%2C34%29%0D%0A%29


Since the legs are x and 30 this means that a=x and b=30


Also, since the hypotenuse is 34, this means that c=34.


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


x%5E2%2B30%5E2=34%5E2 Plug in a=x, b=30, c=34


x%5E2%2B900=34%5E2 Square 30 to get 900.


x%5E2%2B900=1156 Square 34 to get 1156.


x%5E2=1156-900 Subtract 900 from both sides.


x%5E2=256 Combine like terms.


x=sqrt%28256%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=16 Simplify the square root.


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Answer:


So the solution is x=16 which means that the other side length is 16 mm