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

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Question 207279: A rectangular parcel of land is 50 ft wide. The length of a diagonal between opposite corner is 10 ft 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!
let width = W = 50
let length = L
let Diagonal = D = L + 10
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The diagonal forms the hypotenuse of a right triangle.
pythagorean formula applies:
a^2 + b^2 = c^2
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a = W
b = L
c = D
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W^2 + L^2 = D^2
W = 50
L = L
D = (L + 10)
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formula becomes:
50^2 + L^2 = (L+10)^2
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this becomes:
2500 + L^2 = L^2 + 10L + 10L + 100 which becomes:
2500 + L^2 = L^2 + 20L + 100
subtract L^2 from both sides of equation to get:
2500 = 20L + 100
subtract 100 from both sides of equation to get:
2400 = 20L
divide both sides of equation by 20 to get:
120 = L which is the same as:
L = 120
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if L = 120, then D = 130
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values for rectangle are now:
L = 120
W = 50
D = 130
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to show this is good, substitute in pythagorean formula again to get:
50^2 + 120^2 = 130^2
simplify to get:
2500 + 14400 = 16900 which becomes:
16900 = 16900 confirming that the values for L and W and D are good.
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