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(35256) 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




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