Question

Which describes the cross section of a square prism that passes through vertices A, B, and C?

Answer 1

Answer:

In triangle ABC one side equal $8\sqrt{2}$ and two sides equal $4\sqrt{13}$

Step-by-step explanation:

We are given a prism whose base is square with sides 8 in and height 12 in.

If we take cross section through vertices A, B and C

We will get a cross section as triangle.

In triangle ABC, sides are AB, BC and AC

AB is diagonal of top square whose side 8 in.

$AB=\sqrt{8^2+8^2}=8\sqrt{2}$

AC is face diagonal of front face.

$AC=\sqrt{8^2+12^2}=4\sqrt{13}$

BC is face diagonal of right face.

$BC=\sqrt{8^2+12^2}=4\sqrt{13}$

AC=BC≠AB

Hence, In triangle ABC one side equal $8\sqrt{2}$ and two side equal $4\sqrt{13}$

Answer 2

The specified cross section is triangular, with two of its sides equal to 4√13 inches and third side being of 8√2 inches.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

$|AC|^2 = |AB|^2 + |BC|^2$

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

So, the cross section will be a triangle, as we can imagine a plane slicing the square prism at A, C and B vertices.

That will give a triangular cross section whose sides are the length of the line segments AC, AB and BC

Due to symmetry, the length of the line segment AC and BC will be same since they're diagonal of congruent rectangles.

Considered the diagram attached below for references to symbol that will be discussed here:

• Finding the length of BC:

The triangle BDC is a right angled triangle, and BC is its hypotenuse, so by using Pythagoras theorem, we get:

$|BC|^2 = |BD|^2 + |DC|^2\\|BC|^2 = 12^2 + 8^2 = 208\\\\|BC| = \sqrt{208} = 4\sqrt{13}\: \rm in.$

(took positive root since |BC| represents length, which is a non-negative quantity).

• Finding the length of AC:

As discussed above, length of AC = length of BC. Thus, we get:

$|AC| = |BC| = \sqrt{208} = 4\sqrt{13}\: \rm in.$

• Finding the length of AB

AB is a diagonal of the square of side length 8 inches.

That means AB is hypotenuse of a right angled triangle whose non-hypotenuse sides are of 8 inches.

Thus, we get:

$|AB|^2 = 8^2 +8^2\\|AB| = \sqrt{2 \times 64} = 8\sqrt{2} \: \rm in.$

Thus, the specified cross section is triangular, with two of its sides equal to 4√13 inches and third side being of 8√2 inches.

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522