Math Problem Statement
Using Pythagoras' theorem, calculate the length of QR. Give your answer to 1 d.p.
Solution
We can solve this problem using Pythagoras' Theorem, which states:
Where is the hypotenuse (the longest side), and and are the other two sides of the right triangle.
Given:
- Hypotenuse () =
- One side () =
- Unknown side () = ?
Rearranging the formula for :
Substituting the values:
Taking the square root:
Final Answer:
The length of is approximately 8.1 cm (to 1 decimal place).
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5 Related Questions:
- How does Pythagoras' theorem work for triangles with different units?
- Can Pythagoras' theorem be used in three dimensions?
- What are some real-world applications of this theorem?
- How do you verify if a triangle is a right triangle using side lengths?
- How would the calculation change if one of the sides was unknown instead of the hypotenuse?
Tip:
Always check that the triangle is a right triangle before applying Pythagoras' theorem!
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Math Problem Analysis
Mathematical Concepts
Geometry
Pythagorean Theorem
Right Triangle Properties
Formulas
c^2 = a^2 + b^2
QR^2 = PQ^2 - PR^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 7-10