If the first term of AP is 4 and the sum of first five term is equal to one-fourth of the sum of the next five term, then find t
1 answer:
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Answer:
inches.
Step-by-step explanation:
The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment .
In this diagram (not to scale,) (length of prism,)
(width of prism,)
(height of prism.)
Pythagorean Theorem can help find the length of , one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.
Start by finding the length of line segment . That's the black dotted line in the diagram. In right triangle
(second diagram,)
- Segment
is the hypotenuse.
- One of the legs of
is
. The length of
, same as the length of this prism.
- Segment
is the other leg of this triangle. The length of
, same as the width of this prism.
Apply the Pythagorean Theorem to right triangle to find the length of
, the hypotenuse of this triangle:
.
Consider right triangle (third diagram.) In this triangle,
- Segment
is the hypotenuse, while
are the two legs.
. The length of segment
is the same as the height of the rectangular prism,
(inches.) Apply the Pythagorean Theorem to right triangle
to find the length of the hypotenuse
:
.
Hence, the length of the longest line segment in this prism is inches.
