Grades 7-8 Video Solutions 2024-2024_7-8

Video Transcription

Video Summary

In solving Daniel's problem with the diagram, we need the top box to have a value of 720, which requires \( n^2 \times \text{something} = 720 \). This means that \( n^2 \) must be a perfect square divisor of 720. We determine that 144, or \( 12^2 \), is the largest perfect square divisor. By checking perfect squares from 1 to \( 12^2 \), the valid ones that are divisors of 720 are 1, 4, 9, 36, and 144. Thus, \( n \) can be values whose squares are these divisors: 1, 2, 3, 4, 6, and 12, totaling six possible values.

Keywords

perfect square divisor

value of n

problem solving

720

diagram