Grades 11-12 Video Solutions 2021-video 2021 11-12/15

Video Transcription

Problem number 15 states, a large triangle is divided into smaller triangles as shown. The number inside each small triangle indicates its perimeter.  What is the perimeter of the large triangle?  So here we have our triangle with the perimeter of each triangle written inside of it. We want to figure out the perimeter of this large triangle.  This perimeter is composed by parts of all of these small triangles colored in blue. But if we add all their perimeters, we would over count the perimeter marked in red.  Do you see something? Luckily we know the exact value that we overshoot the perimeter by because that value is the perimeter of the red triangles.  So to find the yellow perimeter, we add the perimeters of the blue triangles and subtract that of the red triangles. So the final perimeter that we end up getting is 34.  So the question asked us, what is the perimeter of the large triangle? The answer is 34, letter C.

Video Summary

The problem involves finding the perimeter of a large triangle divided into smaller triangles, each marked with its perimeter. To determine the large triangle's perimeter, the perimeters of the blue triangles are summed, but this results in counting the shared edges (the red triangles) twice. To correct this, the perimeter of the red triangles is subtracted from the total perimeter of the blue ones. This calculation leads to a final perimeter of 34 for the large triangle. The correct answer is 34, option C.

Keywords

triangle perimeter

large triangle

blue triangles

red triangles

perimeter calculation