### Brain Teasers

# Dreams of Architecture Students

Jack and Joe are architecture students. For their masterpiece they plan to build an exceptional monument on the plaza of their university.

That plaza has a diameter of 100 meters and has the shape of a perfect circle.

"Lets build an ark that everyone can see from near or far" suggests Jack.

Joe replies, "Nah, that is too common, besides it would be much nicer to combine the roundness with squareness!"

Jack: "I am not even sure if these words really exist, but what do you have in mind, Joe?"

Joe: "I see a giant rectangular triangle. The poles on the circumference of the plaza; And in the upper angle - the right angle - we install a flood light to enlighten the whole plaza!"

Jack: "Fantastic! Because of the upcoming anniversary, we build that triangle 75 meters in height!"

"Do not be ridiculous! That is not possible!" Joe cried out.

Is Joe right? Is it possible or not?

That plaza has a diameter of 100 meters and has the shape of a perfect circle.

"Lets build an ark that everyone can see from near or far" suggests Jack.

Joe replies, "Nah, that is too common, besides it would be much nicer to combine the roundness with squareness!"

Jack: "I am not even sure if these words really exist, but what do you have in mind, Joe?"

Joe: "I see a giant rectangular triangle. The poles on the circumference of the plaza; And in the upper angle - the right angle - we install a flood light to enlighten the whole plaza!"

Jack: "Fantastic! Because of the upcoming anniversary, we build that triangle 75 meters in height!"

"Do not be ridiculous! That is not possible!" Joe cried out.

Is Joe right? Is it possible or not?

### Hint

Thales' theorem### Answer

The maximum height of the rectangular triangle (with the right angle in the air) is defined by the hypotenuse.The largest hypotenuse in the plaza would fit in the exact diameter, namely 100m.

The maximum height is exact the half of the hypotenuse.

So it can only have 50 meters in height.

Joe is right, the rectangular triangle with 75m height is not possible.

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