13. A cube with sides of length s is intersected by a plane that passes through three of the cube's vertices, forming the cross n shown at right. What type of triangle is the cross section? Explain.
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Answer:
The triangle of the cross section is an acute equilateral triangle
Step-by-step explanation:
we know that
An equilateral triangle is a triangle wit three equal internal angles (60 degrees each) and three equal sides
An acute triangle is a triangle with the three interior angles less than 90 degrees
In this problem
The triangle of the cross section is an equilateral triangle and is an acute triangle too
Applying the Pythagoras Theorem find the length side
[tex]d^{2}=s^{2}+s^{2} \\d^{2}=2s^{2}\\d=s\sqrt{2}\ units[/tex]