Which describes the cross section of the cube that passes through the vertices A, B, and C shown below? A cube. The cross section is a triangle. a rectangle that is not a square a square a triangle with three equal sides a triangle with only two equal sides
Answers
Given :- Which describes the cross section of a cube that passes through the vertices A, B, C and D shown below ?
A) A rectangle that is not a square .
B) A square .
C) A parallelogram that is not a rectangle or a square .
D) A trapezoid .
Solution :-
Let us assume that, side of square is a unit .
so, in quadrilateral ABCD, we have,
→ AB = Diagonal of upper face of cube = √2a unit .
→ BC = side of cube = a unit .
→ CD = Diagonal of upper face of cube = √2a unit .
→ DA = side of cube = a unit .
now, we know that,
- Diagonal of a cube = √3a .
so, checking,
→ AB² + DC² = AC²
→ (√2a)² + a² = (√3a)²
→ 2a² + a² = 3a²
→ 3a² = 3a²
therefore, we can conclude that, ∆ADC is a right angled ∆, or angle ADC is equal to 90° .
As we can see that, opposite sides are equal and intersect at 90° .
Hence, we can conclude that, the cross section so formed will be (A) a rectangle that is not a square .
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Answer:
Im pretty sure the answer is B Because it is a square and it can't be a trapezoid nor can it be a rectangle so that leaves me with saying that its a square so its B Hope this helps