Vertical poles

Geometry Level pending

Two vertical poles with heights of 5 5 and 8 8 , respectively, are standing on a horizontal plane. If the distance between their tops is 3 37 3\sqrt{37} , what is the distance between their bottoms?

18 31 14 20 16

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Relevant wiki: Pythagorean Theorem

Consider my diagram. By pythagorean theorem, we have

x = ( 3 37 ) 2 − 3 2 = 333 − 9 = 324 = 18 x=\sqrt{(3\sqrt{37})^2-3^2}=\sqrt{333-9}=\sqrt{324}=\boxed{18}

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