Math Problem Statement
give me answer
Solution
The cuboid in the image has the following dimensions:
To calculate the length of , we need to recognize that is a diagonal in the base of the cuboid formed by the vertices .
Step 1: Recognize the triangle
The points form a right-angled triangle:
- (given),
- is what we need to calculate,
- is the diagonal of rectangle , where .
Step 2: Calculate diagonal
is the diagonal of a rectangle with sides and . Using the Pythagorean theorem for right triangle :
Substitute the values:
Step 3: Use Pythagorean theorem for triangle
Now that we know , we can find . We apply the Pythagorean theorem again, considering the right triangle :
Substitute the values:
Finally, calculate :
Final Answer:
The length of is approximately 17.94 cm.
Would you like more details or explanations on any steps?
Here are 5 related questions to explore:
- How would you calculate the diagonal of a cuboid?
- Can the Pythagorean theorem be applied in three dimensions?
- How would you calculate the surface area of this cuboid?
- What is the formula for the space diagonal of a cuboid?
- How can trigonometry be used to solve cuboid problems?
Tip: Always check if you're working with a right-angled triangle when applying the Pythagorean theorem, as it simplifies calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
3D Shapes
Pythagorean Theorem
Formulas
Diagonal of a rectangle: d = √(a² + b²)
Pythagorean theorem: c² = a² + b²
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-10