Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

I have a strip of paper that is 12 cm long and 2 cm wide. I make a crease across it at 45 degrees and then fold it, so that the two parts of the  strip are aligned in a right angle as shown. What is the shortest possible length in cm of xy? We're going to call z the intersection of the sides of the folded paper, and we'll  show it below. We want to minimize the hypotenuse xy of the right triangle xyz, which occurs when the triangle is isosceles.  Since xy plus zy equals 14, we have that the desired side lengths are 7 cm and 7 cm, and therefore the hypotenuse has length 7 root 2.

Video Summary

I have a strip of paper that is 12 cm long and 2 cm wide. I make a crease across it at 45 degrees and then fold it, so that the two parts of the strip are aligned in a right angle as shown. What is the shortest possible length in cm of xy? We're going to call z the intersection of the sides of the folded paper, and we'll show it below. We want to minimize the hypotenuse xy of the right triangle xyz, which occurs when the triangle is isosceles. Since xy plus zy equals 14, we have that the desired side lengths are 7 cm and 7 cm, and therefore the hypotenuse has length 7 root 2.

Keywords

paper folding

geometry

right triangle

isosceles triangle

hypotenuse