Question

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.

Answer 1

The triangle of the cross section is an acute equilateral triangle

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

`d^(2)=s^(2)+s^(2) \\d^(2)=2s^(2)\\d=s√(2)\ units`