Asked by Toney
A rectangular parcel of land is 70 ft longer than it is wide. Each diagonal between opposite corners is 130 ft. What are the dimensions of the parcel?
Answers
Answered by
Steve
sides are x and x+70
x^2 + (x+70)^2 = 130^2
x^2 + x^2 + 140x + 4900 = 16900
2x^2 + 140x - 12000 = 0
x^2 + 70x - 6000 = 0
(x+120)(x-50) = 0
x = 50
sides are 50, 120
Or, more easily, you could have checked for a scaled-up 5,12,13 triangle. The diagonal of 130 was a good hint.
x^2 + (x+70)^2 = 130^2
x^2 + x^2 + 140x + 4900 = 16900
2x^2 + 140x - 12000 = 0
x^2 + 70x - 6000 = 0
(x+120)(x-50) = 0
x = 50
sides are 50, 120
Or, more easily, you could have checked for a scaled-up 5,12,13 triangle. The diagonal of 130 was a good hint.
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