Question
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
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.