SOLUTION: Dimensions of a Lot A rectangular parcel of land is 50 m wide. The length of a diagonal between opposite corners is 10 m more than the length of the parcel. What is the length of

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Question 1188986: Dimensions of a Lot A rectangular parcel of land is 50 m wide. The length of a diagonal between opposite
corners is 10 m more than the length of the parcel. What is the length of the parcel?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the lot is 50 meters wide.
the length of a diagonal between opposite corners is 10 meters more than the length.

my diagram is shown below that that visualize your problem.

the diagonal forms the length of the hypotenuse of a right triangle whose legs are L and W.
when W = 50 cm, the legs becomes L and 50.
the hypotenuse, being 10 meters more than the length, is equal to L + 10.

by pythagorus, L^2 + 50^2 = (L + 10)^2
simplify to get:
L^2 + 2500 = L^2 + 20L + 100
subtract L^2 from both sides of the eqution to get:
2500 = 20L + 100
subtract 100 from both sides of the equation to get:
2400 = 20L
divide both sides of the equation by 20 to gt:
120 = L
since the hypotenuse is 10 meters more than the length, then the hypotenuse has to be 130.
you get:
120^2 + 50^2 = 130^2
simplify to get:
16900 = 16900.
this confirms the length of the hypotenuse is correct.
this also confirms the length of the rectangle is correct.

your solution is that the length of the parcel is equal to 120 cm.