SOLUTION: What is the area of a rectangle with a length of 45 and diagonals of 51?

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Question 118667: What is the area of a rectangle with a length of 45 and diagonals of 51?
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
If we cut the rectangle in half along the diagonal, we get this triangle


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%2Cx%29%2C%0D%0Alocate%281%2C-0.2%2C45%29%2C%0D%0Alocate%281%2C2%2C51%29%0D%0A%29

Since we can see that the triangle has legs of x and 45 with a hypotenuse of 51, 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



x%5E2%2B45%5E2=51%5E2 Plug in a=x, b=45, and c=51. Now lets solve for x


+x++%5E+2+%2B+2+0+2+5+=+2+6+0+1 Square each individual term



+x++%5E+2+=+2+6+0+1+-+2+0+2+5 Subtract 2025 from both sides


+x++%5E+2+=+5+7+6 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+5+7+6+%29 Take the square root of both sides



x=24 Simplify the square root




So the width is 24


A=24%2A45=1080 Now multiply 24 and 45 to get the area


So the area of the rectangle is 1080