A gymnast performs a tumbling run along the diagonal of a square mat with sides that are 35 feet long. What distance does the gymnast tumble?

1 Answer
Nov 20, 2015

Answer:

#35sqrt2# feet

Explanation:

Refer to the following picture of a square with a diagonal drawn in:

mathamazement.com

When the diagonal is drawn, two triangles with degree measures of #45˚,45˚,90˚# are created. It is very important in geometry to remember that in this situation, where a triangle has those two angle measurements, the hypotenuse is always #sqrt2# times larger than the other two sides, which are congruent.

For example, in a #45˚,45˚,90˚# triangle where the two shortest sides are #11#, the hypotenuse is #11sqrt2#.

This is almost identical to your problem. Each side of the square is #35#, so the diagonal of the square, which is the hypotenuse of the #45˚,45˚,90˚# triangle is just #sqrt2xx35# feet#=35sqrt2# feet.