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:

c2=a2+b2c^2 = a^2 + b^2

Where cc is the hypotenuse (the longest side), and aa and bb are the other two sides of the right triangle.

Given:

  • Hypotenuse (PQPQ) = 9cm9 \, \text{cm}
  • One side (PRPR) = 4cm4 \, \text{cm}
  • Unknown side (QRQR) = ?

Rearranging the formula for QRQR:

QR2=PQ2PR2QR^2 = PQ^2 - PR^2

Substituting the values:

QR2=9242QR^2 = 9^2 - 4^2

QR2=8116QR^2 = 81 - 16

QR2=65QR^2 = 65

Taking the square root:

QR=658.1cmQR = \sqrt{65} \approx 8.1 \, \text{cm}

Final Answer:

The length of QRQR is approximately 8.1 cm (to 1 decimal place).


Would you like further details or clarifications? 😊

5 Related Questions:

  1. How does Pythagoras' theorem work for triangles with different units?
  2. Can Pythagoras' theorem be used in three dimensions?
  3. What are some real-world applications of this theorem?
  4. How do you verify if a triangle is a right triangle using side lengths?
  5. 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