Square Lot

Al and Curt live at opposite corners of a square lot; Beth and Dawn live at the other two corners. They all carry water from a spring S located within the lot. The spring is 50 feet from Al, 30 feet from Beth, and 40 feet from Curt. How far is the spring from Dawn?
Source: NCTM Mathematics Teacher 2008


a^2+b^2=x^2\qquad\:\: (1)
a^2+c^2=50^2\qquad (2)
c^2+d^2=30^2\qquad (3)
b^2+d^2=40^2\qquad (4)
Subtract Eq. (2) from Eq. (1)
b^2-c^2=x^2-50^2\qquad\:\: (5)
Subtract Eq. (3) from Eq. (4)
b^2-c^2=40^2-30^2\qquad (6)
Compare Eq. (5) and Eq. (6)
x=56.6 feet

Answer: 56.6 feet


About mvtrinh

Retired high school math teacher.
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