SOLUTION: A rectangular parcel of land is 50 ft wide. The length of a diagonla between opposite corners is 10 ft more than the lenght of the parcel. What is the lenght of the parcel?

Question 23845: A rectangular parcel of land is 50 ft wide. The length of a diagonla between opposite corners is 10 ft more than the lenght of the parcel. What is the lenght of the parcel?
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
If we draw the rectangle with width=50, length=x, diagonal=x+10, we find a right triangle with sides 50 and x, and hypotenuse=x+10. We then use the Pythagorean Theorem to get (x+10)^2 = 50^2 + x^2, so x^2+20x+100=2500+x^2.
When we subtract x^2 from both sides, we get 20x+100=2500, subtracting 100 gives 20x=2400, dividing by 20 gives x=120ft. So this is the length.
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