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

Video Transcription

A point P is chosen inside an equilateral triangle. From P, we draw three segments parallel to the sides as shown. The lengths of the segments are 2m, 3m, and 6m.  What is the perimeter of the triangle? Let's extend segments through P. For example, extending this length 6 segment, extending  the length 2 segment, and extending the length 3 segment will give us three new equilateral triangles.  Then because we know that this side has length 6, and this bottom side also has 2, and this  bottom side has length 3, then one side of the original triangle has length 11, and therefore the perimeter of the triangle is 33.

Video Summary

The problem involves an equilateral triangle with point P inside it. From P, three segments are drawn parallel to the sides of the triangle with lengths 2m, 3m, and 6m. By extending these segments, three new equilateral triangles are formed, where the segments determine the lengths of new triangle sides. The original triangle's side length is found by adding the lengths of these segments: 2 + 3 + 6 = 11m. Thus, the perimeter of the original equilateral triangle is 3 times the side length, resulting in a perimeter of 33m.

Keywords

equilateral triangle

point P

parallel segments

triangle side length

perimeter