The right triangles with the perpendicular sides (3cm,4cm),(4cm,5cm) and (5cm,3cm) are wided together so that the sides of equal length come together. The volume of resultant solid is
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Ben gave you a good answer with very a nice diagram. The fold-mark described in the question is 3.75 cm long.
The diagonal of that rectangular piece of paper is 5 cm long but is not described as a fold line in the question.
There are, of course, other ways to solve the problem and get to the, same answer.
If the problem is part of a geometry course, a geometry-based “show-your-work” explanation would be expected, and Ben's is a good one. It uses the fact that 3–4–5 right triangles are formed by drawing the diagonal, and the smaller right triangles having that diagonal and the fold-line for sides are smaller, scaled-down 3–4–5 versions of the 3cn-4cm-5cm triangles.
Other ways to get to the same answer are possible, but if you use trigonometry or analytical geometry, you should understand that any memorized “formula” you use is based on geometry.
I believe those 3cm-4cm-5cm right triangles formed by the sides and the diagonal are fundamental to any answer, as the Pythagorean theorem is needed to calculate that the length of the diagonal is 5 cm.
An alternate geometry-based “show-your-work” answer can be written using larger 3–4–5 right triangles. If you extend the lines along the long sides of the 3 by 4 piece of paper, and draw a line parallel to the fold-line from one end of the diagonal, you form a larger 3–4–5 triangle. In that larger 3–4–5 right triangle, the shorter side/leg, parallel and congruent to (same length as) the fold-line is 3/4 as long as the long leg (the 5-cm diagonal). So, its length can be calculated as
(3/4)(5cm) = 3.75cm
The diagonal of that rectangular piece of paper is 5 cm long but is not described as a fold line in the question.
There are, of course, other ways to solve the problem and get to the, same answer.
If the problem is part of a geometry course, a geometry-based “show-your-work” explanation would be expected, and Ben's is a good one. It uses the fact that 3–4–5 right triangles are formed by drawing the diagonal, and the smaller right triangles having that diagonal and the fold-line for sides are smaller, scaled-down 3–4–5 versions of the 3cn-4cm-5cm triangles.
Other ways to get to the same answer are possible, but if you use trigonometry or analytical geometry, you should understand that any memorized “formula” you use is based on geometry.
I believe those 3cm-4cm-5cm right triangles formed by the sides and the diagonal are fundamental to any answer, as the Pythagorean theorem is needed to calculate that the length of the diagonal is 5 cm.
An alternate geometry-based “show-your-work” answer can be written using larger 3–4–5 right triangles. If you extend the lines along the long sides of the 3 by 4 piece of paper, and draw a line parallel to the fold-line from one end of the diagonal, you form a larger 3–4–5 triangle. In that larger 3–4–5 right triangle, the shorter side/leg, parallel and congruent to (same length as) the fold-line is 3/4 as long as the long leg (the 5-cm diagonal). So, its length can be calculated as
(3/4)(5cm) = 3.75cm
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