The lengths of three sides of a right triangle are all integer numbers.
a) Show that one of them is divisible by \(3\).
b*) Show that one of them is divisible by \(5\).
A segment \(AB\) is a base of an isosceles triangle \(ABC\). A line perpendicular to the segment \(AC\) was drawn through point \(A\) – this line crosses an extension of the segment \(BC\) at point \(D\). There is also a point \(E\) somewhere, such that angles \(\angle ECB\) and \(\angle EBA\) are both right. Point \(F\) is on the extension of the segment \(AB\), such that \(B\) is between \(A\) and \(F\). We also know that \(BF = AD\). Show that \(ED =EF\).
The length of the hypotenuse of a right-angled triangle is 3.
a) The Scattered Scientist calculated the dispersion of the lengths of the sides of this triangle and found that it equals 2. Was he wrong in the calculations?
b) What is the smallest standard deviation of the sides that a rectangular triangle can have? What are the lengths of its sides, adjacent to the right angle?