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

Video Transcription

Harsh makes a net using a combination of squares and equilateral triangles as shown in the figure. The side length of each square and of each triangle is 1 cm.  He folds the net up into the solid shown. What is the distance between vertices A and B? So note that the four vertices joined to A form a square CDEF of side 1 cm long.  Then by the Pythagorean theorem we know that the diagonal CE must be root 2 cm long. Let M then be the midpoint of CE which extends up to A vertically.  Then AMC must be a right triangle with hypotenuse AC of length 1 cm and like CM of length root 2 over 2 cm.  Then we can use the Pythagorean theorem to find that AM has length root 2 over 2 cm and thus we find that the distance between A and B must be root 2 over 2 plus 1 with another  root 2 over 2 on the other side for a total length of 1 plus root 2.

Video Summary

Harsh makes a net using a combination of squares and equilateral triangles as shown in the figure. The side length of each square and of each triangle is 1 cm. He folds the net up into the solid shown. What is the distance between vertices A and B? So note that the four vertices joined to A form a square CDEF of side 1 cm long. Then by the Pythagorean theorem we know that the diagonal CE must be root 2 cm long. Let M then be the midpoint of CE which extends up to A vertically. Then AMC must be a right triangle with hypotenuse AC of length 1 cm and like CM of length root 2 over 2 cm. Then we can use the Pythagorean theorem to find that AM has length root 2 over 2 cm and thus we find that the distance between A and B must be root 2 over 2 plus 1 with another root 2 over 2 on the other side for a total length of 1 plus root 2.

Keywords

net

squares

equilateral triangles

Pythagorean theorem

distance