Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

Video Summary

The solution calculates the number of integer pairs \((m, n)\) where the area of triangle OPQ equals 2024, given \(m\) and \(n\) are integers such that \(0 < m < n\). Employing the shoelace method, the area is determined to be \(\frac{1}{2}(n^2 - m^2)\). For the area to be 2024, the expression \(n^2 - m^2\) must be 4048. Since \(n + m\) and \(n - m\) must both either be even or both be odd, this expression is broken down into six possible pairs of integer factors. Thus, there are six valid pairs of \((m, n)\).

Keywords

integer pairs

triangle area

shoelace method

factor pairs

solution calculation